🔗 Problem

Problem: A child builds a sandcastle in a sandbox. The sandbox has the shape of a cubic box with 512 cubic feet of sand. What is the length of each side of the sandbox in feet?

GPT-4o:

    To find the length of each side of the cubic sandbox, we need to determine the cube root of the volume. The volume of the sandbox is given as 512 cubic feet.

    The formula for the volume \( V \) of a cube with side length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 512 \) cubic feet, we need to solve for \( s \):
    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    We can determine the cube root of 512 by recognizing that:
    \[ 512 = 8 \times 8 \times 8 = 8^3 \]

    Thus:
    \[ \sqrt[3]{512} = 8 \]

    Therefore, the length of each side of the sandbox is 8 feet.

    ### Answer: 8 feet

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: An artisan carves a cubic fireplace out of stone, which has a volume of 729 cubic feet. What is the length of each side of the fireplace in feet?

GPT-4o:

    To find the length of each side of the cubic fireplace, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 729 \, \text{cubic feet} \]

    We need to find \( s \) such that:
    \[ s^3 = 729 \]

    To find \( s \), we take the cube root of 729:
    \[ s = \sqrt[3]{729} \]

    We know that:
    \[ 9 \times 9 \times 9 = 729 \]

    Therefore:
    \[ \sqrt[3]{729} = 9 \]

    So, the length of each side of the fireplace is 9 feet.

    ### Answer: 9 feet

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: A farmer has a large cubical barn with a volume of 1000 cubic meters. What is the length of each side of the barn in meters?

GPT-4o:

    To find the length of each side of the cubical barn, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by:

    \[ V = s^3 \]

    where \( s \) is the length of each side. Given that the volume \( V \) is 1000 cubic meters, we can set up the equation:

    \[ s^3 = 1000 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1000} \]

    We know that:

    \[ 10^3 = 1000 \]

    Therefore:

    \[ \sqrt[3]{1000} = 10 \]

    So, the length of each side of the barn is 10 meters.

    ### Answer: 10 meters

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A giraffe's tank in the zoo is in a cubic shape in order to facilitate its movement. The volume of the tank is 512 m^3. If all sides of the tank are equal in size, what is the size of one side of the tank in meters?

GPT-4o:

    To find the size of one side of the cubic tank, we need to determine the cube root of the volume. The volume of the tank is given as 512 cubic meters.

    The formula for the volume \( V \) of a cube with side length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 512 \) m\(^3\), we need to solve for \( s \):
    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    We can calculate the cube root of 512:
    \[ 512 = 8 \times 8 \times 8 \]
    \[ \sqrt[3]{512} = 8 \]

    Thus, the size of one side of the tank is 8 meters.

    ### Answer: 8 meters

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A mountain has a cuboidal shape and its volume is 64 km^3. If all of the sides of this cuboid are of equal length, what is the length of each side in kilometers?

GPT-4o:

    To find the length of each side of the cuboidal mountain, we need to determine the side length of a cube with the same volume.

    Given that the volume of the cuboid (which is a cube in this case) is 64 km³, we can use the formula for the volume of a cube:
    \[ V = s^3 \]
    where \( V \) is the volume and \( s \) is the side length.

    We know:
    \[ 64 = s^3 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{64} \]

    Calculating the cube root of 64:
    \[ s = 4 \]

    Thus, the length of each side of the cuboid is 4 kilometers.

    ### Answer: 4 km

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: There's a large crater on the moon that has a cubic shape and a volume of 512 cubic kilometers. What is the length of each edge of this crater in kilometers?

GPT-4o:

    To find the length of each edge of a cubic crater with a volume of 512 cubic kilometers, we need to determine the cube root of the volume.

    The volume \( V \) of a cube is given by:
    \[ V = s^3 \]
    where \( s \) is the length of each edge.

    Given \( V = 512 \) cubic kilometers, we need to solve for \( s \):
    \[ s^3 = 512 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    We know that:
    \[ 8^3 = 8 \times 8 \times 8 = 512 \]

    Therefore:
    \[ s = 8 \]

    ### Answer: 8 kilometers

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A baby is playing with blocks, assembling them to build a larger cube structure. If the total number of blocks is 343, what is the length (represented in blocks) of one side of the cube?

GPT-4o:

    To determine the length of one side of the cube, we need to find the cube root of the total number of blocks. The total number of blocks is given as 343.

    The cube root of a number \( n \) is a value \( x \) such that \( x^3 = n \).

    Let's find the cube root of 343:

    \[
    x = \sqrt[3]{343}
    \]

    We can test small integers to find the cube root:

    \[
    7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343
    \]

    Thus, the cube root of 343 is 7.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: An alien in a UFO spies a cubic container with a mysterious substance on earth. The volume of the substance is 512 cubic feet. The alien wonders, what is the length of one side of the cubic container in feet?

GPT-4o:

    To find the length of one side of a cubic container, we need to determine the cube root of the volume. The volume of the cubic container is given as 512 cubic feet.

    The formula for the volume \( V \) of a cube with side length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 512 \) cubic feet, we need to solve for \( s \):
    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    Calculating the cube root of 512:
    \[ \sqrt[3]{512} = 8 \]

    Thus, the length of one side of the cubic container is 8 feet.

    ### Answer: 8 feet

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A pencil manufacturer makes pencil-eraser cubes and the volume of each cube is found to be 512 mm^3. What is the edge length of each eraser cube?

GPT-4o:

    To find the edge length of each eraser cube, we need to determine the cube root of the volume. The volume of a cube is given by \( V = a^3 \), where \( a \) is the edge length.

    Given:
    \[ V = 512 \, \text{mm}^3 \]

    We need to find \( a \) such that:
    \[ a^3 = 512 \]

    Taking the cube root of both sides:
    \[ a = \sqrt[3]{512} \]

    We can calculate the cube root of 512:
    \[ 512 = 8 \times 8 \times 8 \]
    \[ \sqrt[3]{512} = 8 \]

    Thus, the edge length of each eraser cube is 8 mm.

    ### Answer: 8 mm

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: The letter G in a certain font uses a cube as a model for its design. If the volume of this cubic model is 8 cubic cm, what is the length of each side of the cube in cm?

GPT-4o:

    To find the length of each side of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 8 cubic cm, we can set up the equation:

    \[ s^3 = 8 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{8} \]

    Since \( 2^3 = 8 \), we have:

    \[ \sqrt[3]{8} = 2 \]

    Therefore, the length of each side of the cube is 2 cm.

    ### Answer: 2 cm

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A shark's territory within the ocean is allotted in the shape of a cube with a volume of 27 cubic kilometers. Can you calculate the length in kilometers of one edge of this cube?

GPT-4o:

    To find the length of one edge of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one edge.

    Given that the volume \( V \) is 27 cubic kilometers, we set up the equation:

    \[ 27 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{27} \]

    Since \( 3^3 = 27 \), we find:

    \[ s = 3 \]

    Thus, the length of one edge of the cube is 3 kilometers.

    ### Answer: 3 kilometers

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A deck of cards is designed in a cubic box. The volume of the box is 1 cubic inch. What is the length of each side of the box in inches?

GPT-4o:

    To find the length of each side of a cubic box with a volume of 1 cubic inch, we need to determine the cube root of the volume.

    The volume \( V \) of a cube is given by:
    \[ V = s^3 \]
    where \( s \) is the length of each side of the cube.

    Given that the volume \( V \) is 1 cubic inch, we have:
    \[ 1 = s^3 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we get:
    \[ s = 1 \]

    ### Answer: 1 inch

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: A unique type of flower grows in the shape of a cube. Each cubic centimeter of this flower holds 1 milliliter of nectar. If a particular flower holds 125 milliliters of nectar, what is the length of one side of this cubic flower in centimeters?

GPT-4o:

    To determine the length of one side of the cubic flower, we need to find the cube root of the volume of the flower. The volume of the flower is given as 125 milliliters, which is equivalent to 125 cubic centimeters.

    The formula for the volume \( V \) of a cube with side length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 125 \) cubic centimeters, we need to solve for \( s \):
    \[ s^3 = 125 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{125} \]

    We know that:
    \[ 5 \times 5 \times 5 = 125 \]

    Therefore:
    \[ \sqrt[3]{125} = 5 \]

    So, the length of one side of the cubic flower is 5 centimeters.

    ### Answer: 5 centimeters

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: In a forest, the volume of a cubical tree stump was found to be 125 cubic meters. What is the length of one side of the tree stump?

GPT-4o:

    To find the length of one side of a cubical tree stump, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of one side.

    Given the volume \( V = 125 \) cubic meters, we need to solve for \( s \):

    \[ s^3 = 125 \]

    Taking the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5^3 = 5 \times 5 \times 5 = 125 \]

    Therefore:

    \[ \sqrt[3]{125} = 5 \]

    ### Answer: 5 meters

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A jeweler is designing a bracelet in the shape of a cube. The volume of the bracelet is 1000 cubic millimeters. What is the length of each edge of the bracelet in millimeters?

GPT-4o:

    To find the length of each edge of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each edge. Given that the volume \( V \) is 1000 cubic millimeters, we can set up the equation:

    \[ 1000 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1000} \]

    We know that:

    \[ 10 \times 10 \times 10 = 1000 \]

    Thus:

    \[ \sqrt[3]{1000} = 10 \]

    So, the length of each edge of the bracelet is 10 millimeters.

    ### Answer: 10 millimeters

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A bar of soap is in the shape of a cube. If its volume is 1 cubic cm, what is the length of each side of the soap in cm?

GPT-4o:

    To find the length of each side of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 1 cubic cm, we can set up the equation:

    \[ 1 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:

    \[ s = 1 \]

    ### Answer: 1 cm

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: A forest ranger discovered a rare cubic yew tree with a volume of 216 cubic meters. What is the length of each edge of this yew tree in meters?

GPT-4o:

    To find the length of each edge of the cubic yew tree, we need to determine the side length of a cube with a volume of 216 cubic meters.

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]
    where \( s \) is the length of each edge of the cube.

    Given that the volume \( V \) is 216 cubic meters, we can set up the equation:
    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:
    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of each edge of the cubic yew tree is 6 meters.

    ### Answer: 6 meters

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A blanket is folded in a perfect cube shape and has a volume of 1000 cubic cm. What is the length of each side of the blanket in centimeters?

GPT-4o:

    To find the length of each side of the blanket, we need to determine the side length of a cube with a volume of 1000 cubic centimeters. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. We are given that \( V = 1000 \) cubic centimeters. Therefore, we need to solve for \( s \):

    \[ s^3 = 1000 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1000} \]

    The cube root of 1000 is 10 because:

    \[ 10^3 = 10 \times 10 \times 10 = 1000 \]

    Thus, the length of each side of the blanket is 10 centimeters.

    ### Answer: 10 centimeters

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A toy train is positioned inside a box, which is a cube. The volume of the box is 125 cubic centimeters. What is the length of each side of the box in centimeters?

GPT-4o:

    To find the length of each side of the cube, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 125 cubic centimeters, we can set up the equation:

    \[ 125 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5 \times 5 \times 5 = 125 \]

    Therefore:

    \[ \sqrt[3]{125} = 5 \]

    So, the length of each side of the box is 5 centimeters.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A perfume bottle is shaped like a cube and it has a volume of 125 cubic centimeters. What is the length of each side of the bottle in centimeters?

GPT-4o:

    To find the length of each side of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 125 cubic centimeters, we set up the equation:

    \[ 125 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5 \times 5 \times 5 = 125 \]

    Thus:

    \[ \sqrt[3]{125} = 5 \]

    So, the length of each side of the bottle is 5 centimeters.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A pencil-shaped building has a cuboidal structure. The building has a uniform cross-sectional area all along its height. When the volume of the building is calculated, it comes out to be 216 cubic meters. If the building height, width and depth are all equal, what is the length in meters of one side?

GPT-4o:

    Given that the building is cuboidal and has equal height, width, and depth, it is essentially a cube. Let's denote the side length of the cube by \( s \).

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]

    We are given that the volume of the building is 216 cubic meters:
    \[ s^3 = 216 \]

    To find the side length \( s \), we need to take the cube root of 216:
    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:
    \[ 216 = 6 \times 6 \times 6 \]
    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of one side of the building is:
    ### Answer: 6 meters.

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A chair is designed in the shape of a cube, and its volume is 343 cubic feet. What is the length of each side of the chair in feet?

GPT-4o:

    To find the length of each side of the chair, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 343 \, \text{cubic feet} \]

    We need to find \( s \) such that:
    \[ s^3 = 343 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{343} \]

    We know that:
    \[ 7 \times 7 \times 7 = 343 \]

    Therefore:
    \[ \sqrt[3]{343} = 7 \]

    ### Answer: 7 feet

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A roller skate company designs a new line of cubes that will go on the end of each skate. The volume of each cube is calculated to be 729 cubic inches. What is the length, in inches, of a side of each cube?

GPT-4o:

    To find the length of a side of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of a side.

    Given that the volume \( V \) is 729 cubic inches, we set up the equation:

    \[ 729 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{729} \]

    We need to find the cube root of 729. We can do this by recognizing that:

    \[ 729 = 9 \times 9 \times 9 \]

    Thus,

    \[ \sqrt[3]{729} = 9 \]

    So, the length of a side of each cube is 9 inches.

    ### Answer: 9 inches

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: An alien species uses cubical spaceships for traveling. The volume of one of these spaceships is 8 cubic miles. What is the length in miles of each edge of the spaceship?

GPT-4o:

    To find the length of each edge of the cubical spaceship, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of each edge.

    Given:
    \[ V = 8 \text{ cubic miles} \]

    We need to find \( s \) such that:
    \[ s^3 = 8 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{8} \]

    Since \( 2^3 = 8 \):
    \[ \sqrt[3]{8} = 2 \]

    Thus, the length of each edge of the spaceship is 2 miles.

    ### Answer: 2 miles

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A strawberry farmer builds a cube-shaped cold storage unit for his strawberries. The cold storage has a volume of 343 cubic feet. What is the length of each side of the storage unit in feet?

GPT-4o:

    To find the length of each side of the cube-shaped cold storage unit, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 343 \, \text{cubic feet} \]

    We need to find \( s \) such that:
    \[ s^3 = 343 \]

    To find \( s \), we take the cube root of 343:
    \[ s = \sqrt[3]{343} \]

    We know that:
    \[ 7 \times 7 \times 7 = 343 \]

    Therefore:
    \[ \sqrt[3]{343} = 7 \]

    So, the length of each side of the storage unit is 7 feet.

    ### Answer: 7 feet

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: The volume of the compass cube is 8 cubic inches. What is the length of the edge of the compass cube in inches?

GPT-4o:

    To find the length of the edge of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the length of an edge.

    Given that the volume \( V \) is 8 cubic inches, we set up the equation:

    \[ 8 = a^3 \]

    To solve for \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{8} \]

    Since \( 2^3 = 8 \), we find:

    \[ \sqrt[3]{8} = 2 \]

    Thus, the length of the edge of the compass cube is 2 inches.

    ### Answer: 2 inches

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A potato farmer has a unique farm and prefers to grow his potatoes in cubic plots. One plot has a volume that measures 729 cubic meters. What is the length of each side of the plot in meters?

GPT-4o:

    To find the length of each side of the cubic plot, we need to determine the cube root of the volume. The volume of the cubic plot is given as 729 cubic meters.

    The formula for the volume \( V \) of a cube with side length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 729 \) cubic meters, we need to solve for \( s \):
    \[ s^3 = 729 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{729} \]

    We can determine the cube root of 729 by recognizing that:
    \[ 729 = 9 \times 9 \times 9 \]
    \[ 729 = 9^3 \]

    Thus:
    \[ \sqrt[3]{729} = 9 \]

    Therefore, the length of each side of the plot is 9 meters.

    ### Answer: 9 meters

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: A slide in the amusement park has a cuboid shape. The volume of this slide is given as 1000 cubic feet. If the slide has the same length, width, and height, what is the length of one side of the slide in feet?

GPT-4o:

    To find the length of one side of the cuboid-shaped slide, we need to determine the side length of a cube with the same volume. Since the slide has the same length, width, and height, it forms a cube.

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]
    where \( s \) is the side length of the cube.

    Given that the volume \( V \) is 1000 cubic feet, we can set up the equation:
    \[ s^3 = 1000 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{1000} \]

    Calculating the cube root of 1000:
    \[ s = 10 \]

    Therefore, the length of one side of the slide is 10 feet.

    ### Answer: 10 feet

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A zookeeper is building a new play cube for the monkeys. The volume of the cube is huge - exactly 512 cubic feet! The zookeeper wants all sides of the play cube to be of equal length. What is the length of each side of the play cube in feet?

GPT-4o:

    To find the length of each side of the play cube, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 512 \text{ cubic feet} \]

    We need to find \( s \) such that:
    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of 512:
    \[ s = \sqrt[3]{512} \]

    We can determine the cube root by recognizing that:
    \[ 512 = 8 \times 8 \times 8 \]
    \[ 512 = 8^3 \]

    Thus:
    \[ \sqrt[3]{512} = 8 \]

    Therefore, the length of each side of the play cube is 8 feet.

    ### Answer: 8 feet

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A magical hat inflates into the shape of a perfect cube. When fully inflated, its volume measures 27 cubic centimeters. Can you figure out the length of one edge of the hat when it is fully inflated?

GPT-4o:

    To find the length of one edge of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of one edge of the cube. Given that the volume \( V \) is 27 cubic centimeters, we can set up the equation:

    \[ s^3 = 27 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{27} \]

    We know that:

    \[ 3^3 = 3 \times 3 \times 3 = 27 \]

    Therefore:

    \[ \sqrt[3]{27} = 3 \]

    So, the length of one edge of the hat when it is fully inflated is 3 centimeters.

    ### Answer: 3 centimeters

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A grape farmer is packing his grapes into cube-shaped containers. If one such container holds 27 grapes, how many grapes does each side of the cube hold?

GPT-4o:

    To determine how many grapes each side of the cube holds, we need to find the cube root of the total number of grapes in the container.

    Given that the container holds 27 grapes, we need to find the cube root of 27.

    The cube root of 27 is calculated as follows:
    \[ \sqrt[3]{27} = 3 \]

    This means each side of the cube holds 3 grapes.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A truck driver transports cargo in a big cube-shaped container. He knows that the volume of the container is given as 216 cubic meters. Can you help him find out the length of one side of the cube container?

GPT-4o:

    To find the length of one side of the cube-shaped container, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of one side of the cube. Given that the volume \( V \) is 216 cubic meters, we can set up the equation:

    \[ 216 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ s = 6 \]

    Thus, the length of one side of the cube container is 6 meters.

    ### Answer: 6 meters

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A cube-shaped bracelet charm has a volume of 64 mm^3. What is the length of each edge of the cube charm in millimeters?

GPT-4o:

    To find the length of each edge of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the length of each edge.

    Given that the volume \( V \) is 64 mm\(^3\), we set up the equation:

    \[ 64 = a^3 \]

    To solve for \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus:

    \[ \sqrt[3]{64} = 4 \]

    So, the length of each edge of the cube is 4 millimeters.

    ### Answer: 4 millimeters

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: If a number is cubed and the result is 64, what is the number?

GPT-4o:

    To find the number that, when cubed, results in 64, we need to solve the equation \( x^3 = 64 \).

    We can find the cube root of 64 to determine the value of \( x \):

    \[
    x = \sqrt[3]{64}
    \]

    Since \( 4^3 = 4 \times 4 \times 4 = 64 \), we have:

    \[
    x = 4
    \]

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: Your petite mug is perfect for hot chocolate and has a cubic shape, accommodating comfy 1 liter of hot drink. Can you tell me, how long, in liters, is each side of the petite mug?

GPT-4o:

    To determine the length of each side of the cubic mug, we need to understand that the volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side of the cube.

    Given that the volume \( V \) is 1 liter, we can set up the equation:

    \[ 1 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:

    \[ s = 1 \]

    Therefore, each side of the petite mug is 1 liter in length.

    ### Answer: 1 liter

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: The volume of a cube-shaped blanket is 343 cubic inches when fully fluffed. What is the length of one side of this fluffed blanket in inches?

GPT-4o:

    To find the length of one side of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one side.

    Given that the volume \( V \) is 343 cubic inches, we can set up the equation:

    \[ 343 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{343} \]

    We know that:

    \[ 7 \times 7 \times 7 = 343 \]

    Thus:

    \[ \sqrt[3]{343} = 7 \]

    So, the length of one side of the cube is 7 inches.

    ### Answer: 7 inches

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A Penguin has stacked ice cubes in a specific way to form a larger perfect cube. The volume of the larger cube made up of smaller cubes is 729 cubic cm. If each side of the smaller ice cube is the same length in cm, what is that length?

GPT-4o:

    To determine the side length of the smaller ice cubes, we first need to find the side length of the larger cube. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the side length of the cube. Given that the volume of the larger cube is 729 cubic cm, we can set up the equation:

    \[ s^3 = 729 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{729} \]

    We know that:

    \[ 9 \times 9 \times 9 = 729 \]

    Therefore:

    \[ \sqrt[3]{729} = 9 \]

    So, the side length of the larger cube is 9 cm. Since the larger cube is made up of smaller cubes and each side of the larger cube is 9 cm, the side length of each smaller cube must be 1 cm.

    ### Answer: 1 cm

Expected answer: 9

Correct? No

🔗 Problem

Problem: A kid on a scooter notices that his new scooter wheel, which has a cubic shape, has a volume of 216 cubic cm. What is the length of each side of the wheel in cm?

GPT-4o:

    To find the length of each side of the cubic wheel, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 216 \, \text{cubic cm} \]

    We need to find \( s \) such that:
    \[ s^3 = 216 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{216} \]

    Calculating the cube root:
    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of each side of the wheel is 6 cm.

    ### Answer: 6 cm

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A butterfly places an egg in a cubic flower bud. The volume of the bud is 216 cubic millimeters. What length, in millimeters, is each edge of this flower bud?

GPT-4o:

    To find the length of each edge of the cubic flower bud, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each edge.

    Given that the volume \( V \) is 216 cubic millimeters, we can set up the equation:

    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of each edge of the flower bud is 6 millimeters.

    ### Answer: 6 millimeters

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A snail carries a shell that is shaped like a cube. The volume of the shell is 27 cm^3. What is the length of each side of the snail's cubical shell in centimeters?

GPT-4o:

    To find the length of each side of the cubical shell, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 27 cm\(^3\), we can set up the equation:

    \[ 27 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{27} \]

    Since \( 3^3 = 27 \), we have:

    \[ \sqrt[3]{27} = 3 \]

    Thus, the length of each side of the snail's cubical shell is 3 centimeters.

    ### Answer: 3 cm

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: For a party, a giant cubic party balloon is being used. If the volume of the balloon is 27 cubic feet, what is the length of one side of the balloon in feet?

GPT-4o:

    To find the length of one side of a cubic balloon, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of one side of the cube. Given that the volume \( V \) is 27 cubic feet, we can set up the equation:

    \[ 27 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{27} \]

    We know that:

    \[ 3^3 = 27 \]

    Therefore:

    \[ \sqrt[3]{27} = 3 \]

    So, the length of one side of the balloon is 3 feet.

    ### Answer: 3 feet

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A firefighter is pumping water out of a cubic tank to fight a fire. If the tank has a volume of 216 cubic feet, what is the length of one edge of the tank in feet?

GPT-4o:

    To find the length of one edge of the cubic tank, we need to determine the cube root of the volume of the tank. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one edge.

    Given that the volume \( V \) is 216 cubic feet, we can set up the equation:

    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ s = 6 \]

    Therefore, the length of one edge of the tank is 6 feet.

    ### Answer: 6 feet

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: You have a cube-shaped box of cards with a volume of 216 cubic inches. What is the length of one side of the box in inches?

GPT-4o:

    To find the length of one side of a cube when given its volume, we need to take the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of one side of the cube. Given that the volume \( V \) is 216 cubic inches, we can set up the equation:

    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of one side of the box is 6 inches.

    ### Answer: 6 inches

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A designer is making a cube-shaped pocket for a skirt. She needs 125 cubic inches of fabric to create this uniquely shaped pocket. What is the length in inches of each edge of the pocket?

GPT-4o:

    To find the length of each edge of the cube-shaped pocket, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each edge.

    Given that the volume \( V \) is 125 cubic inches, we can set up the equation:

    \[ 125 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5 \times 5 \times 5 = 125 \]

    Thus:

    \[ \sqrt[3]{125} = 5 \]

    So, the length of each edge of the pocket is 5 inches.

    ### Answer: 5 inches

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A gardener arranged her flowers in a cube shape for an exhibition. The total number of flowers used was 125. What is the length of each side of the flower cube?

GPT-4o:

    To determine the length of each side of the flower cube, we need to find the cube root of the total number of flowers. The total number of flowers used is 125.

    The cube root of 125 is calculated as follows:
    \[ \sqrt[3]{125} = 5 \]

    This is because:
    \[ 5 \times 5 \times 5 = 125 \]

    Therefore, the length of each side of the flower cube is 5.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A farmer grows cucumbers in the shape of a perfect cube for a special contest. One of his cucumbers has a volume of 1000 cubic centimeters. What is the length in centimeters of a side of this cubic cucumber?

GPT-4o:

    To find the length of a side of a cubic cucumber with a volume of 1000 cubic centimeters, we need to determine the cube root of the volume.

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]
    where \( s \) is the length of a side of the cube.

    Given \( V = 1000 \) cubic centimeters, we need to solve for \( s \):
    \[ s^3 = 1000 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{1000} \]

    We know that:
    \[ 10^3 = 1000 \]

    Therefore:
    \[ \sqrt[3]{1000} = 10 \]

    So, the length of a side of the cubic cucumber is 10 centimeters.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A small airplane has a cargo hold whose volume is 27 cubic meters, and all sides of the hold have equal length. What is the length in meters of one side of this cargo hold?

GPT-4o:

    To find the length of one side of the cargo hold, we need to determine the side length of a cube with a volume of 27 cubic meters. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the side length of the cube. We are given that the volume \( V \) is 27 cubic meters. Therefore, we need to solve for \( s \) in the equation:

    \[ 27 = s^3 \]

    To find \( s \), we take the cube root of both sides of the equation:

    \[ s = \sqrt[3]{27} \]

    The cube root of 27 is 3, because:

    \[ 3^3 = 3 \times 3 \times 3 = 27 \]

    Thus, the length of one side of the cargo hold is:

    ### Answer: 3 meters.

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A cucumber farmer is experimenting with a new variety of cucumbers that grow in a perfect cubic shape. One of these cubic cucumbers has a volume of 216 cubic centimeters. What is the length of each side of this cubic cucumber in centimeters?

GPT-4o:

    To find the length of each side of the cubic cucumber, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side. Given that the volume \( V \) is 216 cubic centimeters, we can set up the equation:

    \[ 216 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    We can determine the cube root of 216 by recognizing that:

    \[ 216 = 6 \times 6 \times 6 = 6^3 \]

    Thus,

    \[ \sqrt[3]{216} = 6 \]

    So, the length of each side of the cubic cucumber is 6 centimeters.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A skateboard company designs a cubic box to ship its skateboards. If the volume of the box is 729 cubic feet, what is the length of one edge of the box (in feet)?

GPT-4o:

    To find the length of one edge of a cubic box, we need to determine the cube root of the volume. The volume of the box is given as 729 cubic feet.

    The formula for the volume \( V \) of a cube with edge length \( s \) is:
    \[ V = s^3 \]

    Given \( V = 729 \) cubic feet, we need to solve for \( s \):
    \[ s^3 = 729 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{729} \]

    We know that:
    \[ 9 \times 9 \times 9 = 729 \]

    Thus:
    \[ \sqrt[3]{729} = 9 \]

    Therefore, the length of one edge of the box is 9 feet.

    ### Answer: 9 feet

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: The number 27 appears in a dream of a person who loves cryptic letters. He knows this number corresponds to a number obtained by cubing a letter's position in the alphabet. Can you find that letter by its position? (Let's use 'a' as 1, 'b' as 2, and so on.)

GPT-4o:

    To find the letter corresponding to the number 27, we need to determine which letter's position in the alphabet, when cubed, equals 27.

    Let's denote the position of the letter as \( n \). We need to solve the equation:
    \[ n^3 = 27 \]

    Taking the cube root of both sides, we get:
    \[ n = \sqrt[3]{27} \]

    Since \( 27 = 3^3 \), we have:
    \[ n = 3 \]

    The letter in the 3rd position of the alphabet is 'c'.

    ### Answer: c

Expected answer: 3

Correct? No

🔗 Problem

Problem: A company manufactures small cubical buoys for use in boating. One buoy has a volume of 1 cubic foot. What is the length of each side of the buoy in feet?

GPT-4o:

    To find the length of each side of a cubical buoy with a volume of 1 cubic foot, we need to use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side of the cube.

    Given that the volume \( V \) is 1 cubic foot, we can set up the equation:

    \[ 1 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:

    \[ s = 1 \]

    ### Answer: 1 foot

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: The sun emits rays of energy that heat a cubical object to a temperature of 729 degrees. If the temperature at the heart of this object is directly proportional to the cube of its length, what is the length of the object in units?

GPT-4o:

    Given that the temperature at the heart of the cubical object is directly proportional to the cube of its length, we can express this relationship as:

    \[ T = k \cdot L^3 \]

    where \( T \) is the temperature, \( L \) is the length of the object, and \( k \) is the proportionality constant.

    We are given:
    \[ T = 729 \]

    We need to find \( L \). First, we solve for \( k \):

    \[ 729 = k \cdot L^3 \]

    Since we need to find \( L \), we can assume \( k = 1 \) for simplicity (as the problem does not provide additional information about \( k \)). Thus:

    \[ 729 = L^3 \]

    To find \( L \), we take the cube root of both sides:

    \[ L = \sqrt[3]{729} \]

    We know that:

    \[ 729 = 9^3 \]

    Therefore:

    \[ L = 9 \]

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: An orange was shaped perfectly into a cube, with its volume being 8 cubic centimeters. What is the length of each side of the cube-shaped orange in centimeters?

GPT-4o:

    To find the length of each side of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 8 cubic centimeters, we set up the equation:

    \[ 8 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{8} \]

    The cube root of 8 is 2, because:

    \[ 2^3 = 2 \times 2 \times 2 = 8 \]

    Thus, the length of each side of the cube-shaped orange is 2 centimeters.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A particular telescope has a cubical mirror box where the volume of the box is 729 cubic centimeters. What is the length of one edge of this box, in centimeters?

GPT-4o:

    To find the length of one edge of a cubical box, we need to determine the cube root of the volume. Given that the volume of the cubical mirror box is 729 cubic centimeters, we can set up the equation:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one edge of the cube. Substituting the given volume:

    \[ 729 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{729} \]

    We know that:

    \[ 9 \times 9 \times 9 = 729 \]

    Thus:

    \[ \sqrt[3]{729} = 9 \]

    So, the length of one edge of the box is 9 centimeters.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: A backpack has a cubical storage compartment. The volume of this compartment is 125 cubic inches. What is the length of one side of the compartment in inches?

GPT-4o:

    To find the length of one side of the cubical storage compartment, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of one side.

    Given:
    \[ V = 125 \text{ cubic inches} \]

    We need to find \( s \) such that:
    \[ s^3 = 125 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{125} \]

    We know that:
    \[ 5^3 = 5 \times 5 \times 5 = 125 \]

    Therefore:
    \[ \sqrt[3]{125} = 5 \]

    ### Answer: 5 inches

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A particular model of a stuffed animal comes in a cube-shaped box. The volume of this box is 343 cubic inches. What is the length of each side of the box, in inches?

GPT-4o:

    To find the length of each side of the cube-shaped box, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 343 cubic inches, we can set up the equation:

    \[ 343 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{343} \]

    We know that:

    \[ 7 \times 7 \times 7 = 343 \]

    Thus:

    \[ \sqrt[3]{343} = 7 \]

    Therefore, the length of each side of the box is 7 inches.

    ### Answer: 7 inches

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A certain type of candy comes in cube-shaped packages. When you measured the volume of one of these packages, it turned out to be 512 cubic centimeters. How long is each edge of a candy package?

GPT-4o:

    To find the length of each edge of the cube-shaped candy package, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the length of each edge. Given that the volume \( V \) is 512 cubic centimeters, we can set up the equation:

    \[ 512 = a^3 \]

    To find \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{512} \]

    We can calculate the cube root of 512:

    \[ \sqrt[3]{512} = 8 \]

    Thus, the length of each edge of the candy package is 8 centimeters.

    ### Answer: 8 centimeters

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A solid cube jungle gym at the park has a volume of 512 cubic feet. What is the length of a side of this jungle gym in feet?

GPT-4o:

    To find the length of a side of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of a side.

    Given:
    \[ V = 512 \text{ cubic feet} \]

    We need to find \( s \) such that:
    \[ s^3 = 512 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    We can determine that:
    \[ 512 = 8 \times 8 \times 8 \]
    \[ 512 = 8^3 \]

    Thus:
    \[ \sqrt[3]{512} = 8 \]

    Therefore, the length of a side of the cube is 8 feet.

    ### Answer: 8 feet

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A company designs toothbrushes in a perfect cube shape for easy handling. One model has a volume of 729 cubic centimeters. What is the length of each edge of the toothbrush in centimeters?

GPT-4o:

    To find the length of each edge of the cube-shaped toothbrush, we need to determine the cube root of the volume. The volume of the cube is given as 729 cubic centimeters.

    The formula for the volume of a cube is:
    \[ V = a^3 \]
    where \( V \) is the volume and \( a \) is the length of each edge.

    Given:
    \[ V = 729 \]

    We need to find \( a \) such that:
    \[ a^3 = 729 \]

    To find \( a \), we take the cube root of 729:
    \[ a = \sqrt[3]{729} \]

    Calculating the cube root:
    \[ \sqrt[3]{729} = 9 \]

    Thus, the length of each edge of the toothbrush is 9 centimeters.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: There's a star in a distance galaxy shaped like a perfect cube. Its volume is 8 cubic light years. What is the length of each edge of the star (in light years)?

GPT-4o:

    To find the length of each edge of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each edge.

    Given that the volume \( V \) is 8 cubic light years, we set up the equation:

    \[ s^3 = 8 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{8} \]

    Since \( 2^3 = 8 \), we have:

    \[ \sqrt[3]{8} = 2 \]

    Thus, the length of each edge of the star is 2 light years.

    ### Answer: 2 light years

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A Dolphin can completely fill a cubical chamber with its calls, where the intensity of the call's volume is effectively 1 unit^3. What is the length of each side of the cubical chamber?

GPT-4o:

    To determine the length of each side of the cubical chamber, we need to find the side length of a cube whose volume is 1 cubic unit.

    The formula for the volume \( V \) of a cube is given by:
    \[ V = s^3 \]
    where \( s \) is the length of each side of the cube.

    Given that the volume \( V \) is 1 cubic unit, we can set up the equation:
    \[ s^3 = 1 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:
    \[ s = 1 \]

    ### Answer: 1 unit

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: The volume of a cubic gadget inside a watch mechanism is 1000 mm^3. What is the length of each side of this cubic gadget in millimeters?

GPT-4o:

    To find the length of each side of a cubic gadget, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side. Given that the volume \( V \) is 1000 mm\(^3\), we can set up the equation:

    \[ s^3 = 1000 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1000} \]

    We know that:

    \[ 10^3 = 1000 \]

    Thus:

    \[ \sqrt[3]{1000} = 10 \]

    So, the length of each side of the cubic gadget is 10 millimeters.

    ### Answer: 10 millimeters

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: There is a cube with a volume of 1 cubic meter. Can you find the length of one edge of this cube in meters?

GPT-4o:

    To find the length of one edge of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the length of one edge.

    Given that the volume \( V \) is 1 cubic meter, we set up the equation:

    \[ 1 = a^3 \]

    To solve for \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:

    \[ a = 1 \]

    ### Answer: 1 meter

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: A unicorn keeps her treasure in a magical cube-shaped box. The box has a volume of 216 cubic meters. How long is each side of this box in meters?

GPT-4o:

    To find the length of each side of the cube-shaped box, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 216 cubic meters, we can set up the equation:

    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ \sqrt[3]{216} = 6 \]

    Therefore, the length of each side of the box is 6 meters.

    ### Answer: 6 meters

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A cube-shaped house has a volume of 64 cubic feet. What is the length of one side of the house in feet?

GPT-4o:

    To find the length of one side of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one side.

    Given that the volume \( V \) is 64 cubic feet, we can set up the equation:

    \[ 64 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus:

    \[ \sqrt[3]{64} = 4 \]

    So, the length of one side of the house is 4 feet.

    ### Answer: 4 feet

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: The volume of a cubical toothbrush holder is 1000 cubic centimeters. What is the length in centimeters of the edge of the toothbrush holder?

GPT-4o:

    To find the length of the edge of a cubical toothbrush holder given its volume, we need to use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of an edge.

    Given that the volume \( V \) is 1000 cubic centimeters, we can set up the equation:

    \[ 1000 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1000} \]

    Calculating the cube root of 1000:

    \[ s = 10 \]

    So, the length of the edge of the toothbrush holder is 10 centimeters.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A sandwich shop has a signature bread loaf which is in a cubic form. They bake their bread in a cube-shaped oven whose volume is 125 cubic inches. Determine the length of each side of the loaf (f) in inches?

GPT-4o:

    To determine the length of each side of the cubic loaf, we need to find the side length of a cube with a volume of 125 cubic inches.

    The formula for the volume \( V \) of a cube with side length \( f \) is:
    \[ V = f^3 \]

    Given that the volume \( V \) is 125 cubic inches, we can set up the equation:
    \[ f^3 = 125 \]

    To find \( f \), we take the cube root of both sides of the equation:
    \[ f = \sqrt[3]{125} \]

    Since \( 125 = 5^3 \), we have:
    \[ f = 5 \]

    ### Answer: 5 inches

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A special variety of strawberry is shaped like a cube. The strawberry has a volume of 64 cubic millimeters. What is the length of one side of the strawberry in millimeters?

GPT-4o:

    To find the length of one side of the cube-shaped strawberry, we need to determine the cube root of its volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one side.

    Given that the volume \( V \) is 64 cubic millimeters, we can set up the equation:

    \[ 64 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus:

    \[ \sqrt[3]{64} = 4 \]

    So, the length of one side of the strawberry is 4 millimeters.

    ### Answer: 4 millimeters

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A rocket is designed in the shape of a perfect cube. The rocket has a volume of 216 cubic meters. What is the length of each side of the rocket in meters?

GPT-4o:

    To find the length of each side of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 216 cubic meters, we can set up the equation:

    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:

    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of each side of the rocket is 6 meters.

    ### Answer: 6 meters

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A company manufactures cubic lamp bases. Each lamp base has a volume of 512 cubic inches. Find the length of one edge of the base.

GPT-4o:

    To find the length of one edge of a cubic lamp base, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of one edge of the cube. Given that the volume \( V \) is 512 cubic inches, we can set up the equation:

    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of both sides of the equation:

    \[ s = \sqrt[3]{512} \]

    We know that:

    \[ 8 \times 8 \times 8 = 512 \]

    Therefore:

    \[ \sqrt[3]{512} = 8 \]

    So, the length of one edge of the lamp base is 8 inches.

    ### Answer: 8 inches

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A certain species of fish lays eggs in a cubical arrangement. If one fish lays 27 eggs, what is the length of the edge of this cube?

GPT-4o:

    To determine the length of the edge of the cube, we need to find the cube root of the total number of eggs. The total number of eggs is given as 27.

    The formula for the volume of a cube is:
    \[ V = s^3 \]
    where \( V \) is the volume (number of eggs) and \( s \) is the length of the edge of the cube.

    Given \( V = 27 \), we need to solve for \( s \):
    \[ s^3 = 27 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{27} \]

    Since \( 3^3 = 27 \):
    \[ \sqrt[3]{27} = 3 \]

    Thus, the length of the edge of the cube is 3.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: The volume of a mini school bus is 512 cubic meters. If the shape of the bus can be closely approximated as a cube, then what is the length in meters of one edge of this 'cube'?

GPT-4o:

    To find the length of one edge of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of one edge.

    Given:
    \[ V = 512 \, \text{cubic meters} \]

    We need to find \( s \) such that:
    \[ s^3 = 512 \]

    To solve for \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    Calculating the cube root of 512:
    \[ 512 = 8 \times 8 \times 8 \]
    \[ \sqrt[3]{512} = 8 \]

    Thus, the length of one edge of the cube is 8 meters.

    ### Answer: 8 meters

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A giant cubic balloon used in a carnival has a volume of 343 cubic meters. What is the length of each edge of this balloon in meters?

GPT-4o:

    To find the length of each edge of the cubic balloon, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of each edge.

    Given:
    \[ V = 343 \, \text{cubic meters} \]

    We need to find \( s \) such that:
    \[ s^3 = 343 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{343} \]

    We know that:
    \[ 7 \times 7 \times 7 = 343 \]

    Therefore:
    \[ \sqrt[3]{343} = 7 \]

    ### Answer: 7 meters

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A shirt was created in a very unique 3D cube design with a total volume of 343 cubic centimeters. What is the length of one side of this cubic shirt design in centimeters?

GPT-4o:

    To find the length of one side of a cube when given the volume, we use the formula for the volume of a cube, which is:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of one side of the cube.

    Given that the volume \( V \) is 343 cubic centimeters, we can set up the equation:

    \[ 343 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{343} \]

    We know that:

    \[ 7 \times 7 \times 7 = 343 \]

    Thus:

    \[ \sqrt[3]{343} = 7 \]

    So, the length of one side of the cubic shirt design is 7 centimeters.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A roller skate is a cube-shaped container for a certain piece of equipment. It has a volume of 216 cubic inches. What is the length of each side of this roller skate container in inches?

GPT-4o:

    To find the length of each side of a cube-shaped container, we need to determine the cube root of its volume. The volume of the container is given as 216 cubic inches.

    The formula for the volume of a cube is:
    \[ V = s^3 \]
    where \( V \) is the volume and \( s \) is the length of each side.

    Given \( V = 216 \) cubic inches, we need to solve for \( s \):
    \[ s^3 = 216 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:
    \[ s = 6 \]

    Thus, the length of each side of the roller skate container is 6 inches.

    ### Answer: 6 inches

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: There's a cubic water tank which can hold up to 343 cubic meters of water. What is the side length of this cubic water tank?

GPT-4o:

    To find the side length of a cubic water tank that can hold 343 cubic meters of water, we need to determine the cube root of 343.

    The volume \( V \) of a cube is given by:
    \[ V = s^3 \]
    where \( s \) is the side length of the cube.

    Given:
    \[ V = 343 \]

    We need to solve for \( s \):
    \[ s^3 = 343 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{343} \]

    We know that:
    \[ 7^3 = 7 \times 7 \times 7 = 343 \]

    Therefore:
    \[ \sqrt[3]{343} = 7 \]

    ### Answer: 7 meters

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A backpack has a cubical shape and can hold a volume of 216 cubic inches. What is the length of each side of the backpack in inches?

GPT-4o:

    To find the length of each side of a cubical backpack, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 216 \, \text{cubic inches} \]

    We need to find \( s \) such that:
    \[ s^3 = 216 \]

    To solve for \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{216} \]

    Calculating the cube root of 216:
    \[ \sqrt[3]{216} = 6 \]

    Thus, the length of each side of the backpack is 6 inches.

    ### Answer: 6 inches

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A scientist studying a particular type of dinosaur discovered that the volume of the dinosaur's cube-shaped brain was 1 cubic meter. What is the length in meters of each side of the dinosaur's brain's cube structure?

GPT-4o:

    To find the length of each side of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 1 cubic meter, we set up the equation:

    \[ 1 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:

    \[ s = 1 \]

    ### Answer: 1 meter

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: A certain species of flower grows in clusters shaped as perfect cubes. One cluster of flowers has a volume of 1000 cubic centimeters. How long, in centimeters, is the edge of this flower cube?

GPT-4o:

    To find the edge length of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the edge length of the cube.

    Given that the volume \( V \) is 1000 cubic centimeters, we can set up the equation:

    \[ 1000 = a^3 \]

    To find \( a \), we take the cube root of both sides of the equation:

    \[ a = \sqrt[3]{1000} \]

    Calculating the cube root of 1000:

    \[ a = 10 \]

    Thus, the edge length of the flower cube is 10 centimeters.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A princess has a magical cube-shaped box that can hold 512 cubic inches of fairy dust. What is the length of one side of this box in inches?

GPT-4o:

    To find the length of one side of the cube-shaped box, we need to determine the cube root of the volume. The volume of the cube is given as 512 cubic inches.

    The formula for the volume of a cube is:
    \[ V = s^3 \]
    where \( V \) is the volume and \( s \) is the length of one side.

    Given \( V = 512 \) cubic inches, we need to solve for \( s \):
    \[ s^3 = 512 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    Calculating the cube root of 512:
    \[ \sqrt[3]{512} = 8 \]

    Thus, the length of one side of the box is 8 inches.

    ### Answer: 8 inches

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A toy car toy is designed in the shape of a cube. If the toy car has a volume of 64 cubic inches, what is the length in inches of each side of the toy car?

GPT-4o:

    To find the length of each side of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 64 cubic inches, we can set up the equation:

    \[ 64 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus:

    \[ \sqrt[3]{64} = 4 \]

    So, the length of each side of the toy car is 4 inches.

    ### Answer: 4 inches

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A special cube-shaped clock has a volume of 27 cubic inches. What is the length of each side of the clock in inches?

GPT-4o:

    To find the length of each side of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 27 cubic inches, we set up the equation:

    \[ 27 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{27} \]

    The cube root of 27 is 3, because:

    \[ 3^3 = 3 \times 3 \times 3 = 27 \]

    Thus, the length of each side of the cube is 3 inches.

    ### Answer: 3 inches

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A semi-truck has a cuboidal trailer. The volume of the cargo space in the trailer is 8 cubic meters, but the height and width are both the same length. What is the length of a side of this cubical cargo space?

GPT-4o:

    To find the length of a side of the cubical cargo space, we need to determine the side length of a cube that has a volume of 8 cubic meters.

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]
    where \( s \) is the side length of the cube.

    Given that the volume \( V \) is 8 cubic meters, we can set up the equation:
    \[ s^3 = 8 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{8} \]

    The cube root of 8 is 2, because:
    \[ 2^3 = 2 \times 2 \times 2 = 8 \]

    Therefore, the length of a side of the cubical cargo space is 2 meters.

    ### Answer: 2 meters

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A grocer has a cubic box that perfectly fits 343 grapes in it. What is the length of the side of the box marked in grapes?

GPT-4o:

    To determine the length of the side of the cubic box, we need to find the cube root of the total number of grapes, since the box is cubic and fits 343 grapes perfectly.

    The equation to solve is:
    \[ \text{side length}^3 = 343 \]

    Taking the cube root of both sides:
    \[ \text{side length} = \sqrt[3]{343} \]

    We know that:
    \[ 7 \times 7 \times 7 = 343 \]

    Therefore:
    \[ \sqrt[3]{343} = 7 \]

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: The volume of an elephant is approximately 343 cubic meters. If the elephant has a perfect cube shape, what is the length of each side in meters?

GPT-4o:

    To find the length of each side of a cube when given its volume, we need to take the cube root of the volume. The volume \( V \) of a cube with side length \( s \) is given by:

    \[ V = s^3 \]

    Given that the volume \( V \) is 343 cubic meters, we can set up the equation:

    \[ 343 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{343} \]

    We know that:

    \[ 7 \times 7 \times 7 = 343 \]

    Thus:

    \[ \sqrt[3]{343} = 7 \]

    So, the length of each side of the cube is 7 meters.

    ### Answer: 7 meters

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A camera company produces boxes for their cameras that are in the shape of a cube. The volume of each box is 27 cubic centimeters. Find the length of an edge of the box in centimeters.

GPT-4o:

    To find the length of an edge of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the length of an edge.

    Given that the volume \( V \) is 27 cubic centimeters, we set up the equation:

    \[ 27 = a^3 \]

    To solve for \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{27} \]

    The cube root of 27 is 3, because:

    \[ 3^3 = 3 \times 3 \times 3 = 27 \]

    Therefore, the length of an edge of the box is 3 centimeters.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A lion roars in a cube-shaped territory of its own. The volume of the territory is 8 km^3. What is the edge length of this territory in kilometers?

GPT-4o:

    To find the edge length of a cube when given its volume, we use the formula for the volume of a cube:

    \[ V = a^3 \]

    where \( V \) is the volume and \( a \) is the edge length.

    Given that the volume \( V \) is 8 km³, we can set up the equation:

    \[ a^3 = 8 \]

    To solve for \( a \), we take the cube root of both sides:

    \[ a = \sqrt[3]{8} \]

    The cube root of 8 is 2, since:

    \[ 2^3 = 2 \times 2 \times 2 = 8 \]

    Therefore, the edge length of the territory is:

    ### Answer: 2 km

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: In a school, the students use cube-shaped backpacks to carry their books. One of these cube backpacks has a volume of 125 cubic inches. What is the length of each side of the backpack in inches?

GPT-4o:

    To find the length of each side of a cube when given its volume, we need to take the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 125 cubic inches, we can set up the equation:

    \[ 125 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5 \times 5 \times 5 = 125 \]

    Therefore:

    \[ \sqrt[3]{125} = 5 \]

    So, the length of each side of the backpack is 5 inches.

    ### Answer: 5 inches

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A particular superhero has the ability to enclose villains in a cube of energy. If the cube has a volume of 64 cubic meters, what is the length of each side of the cube?

GPT-4o:

    To find the length of each side of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of each side of the cube. Given that the volume \( V \) is 64 cubic meters, we can set up the equation:

    \[ 64 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus:

    \[ \sqrt[3]{64} = 4 \]

    So, the length of each side of the cube is 4 meters.

    ### Answer: 4 meters

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A treasure chest has a cube shape. The volume of the treasure chest is 125 cubic feet. What is the length of each side of the treasure chest in feet?

GPT-4o:

    To find the length of each side of a cube when given the volume, we use the formula for the volume of a cube:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of each side.

    Given that the volume \( V \) is 125 cubic feet, we set up the equation:

    \[ 125 = s^3 \]

    To solve for \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{125} \]

    We know that:

    \[ 5 \times 5 \times 5 = 125 \]

    Thus:

    \[ \sqrt[3]{125} = 5 \]

    So, the length of each side of the treasure chest is 5 feet.

    ### Answer: 5 feet

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A fish tank in the shape of a cube holds exactly 1 cubic meter of water. What is the length, in meters, of each side of the fish tank?

GPT-4o:

    To determine the length of each side of the fish tank, we need to find the side length of a cube that has a volume of 1 cubic meter.

    The volume \( V \) of a cube is given by the formula:
    \[ V = s^3 \]
    where \( s \) is the length of each side of the cube.

    Given that the volume \( V \) is 1 cubic meter, we can set up the equation:
    \[ s^3 = 1 \]

    To find \( s \), we take the cube root of both sides:
    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we have:
    \[ s = 1 \]

    ### Answer: 1 meter

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: A chef is experimenting with cubed food presentations and crafts an appetizer from cheese. The appetizer's volume is 125 cubic centimeters. What is the length of one side of this cheese cube in centimeters?

GPT-4o:

    To find the length of one side of the cheese cube, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of one side.

    Given:
    \[ V = 125 \, \text{cubic centimeters} \]

    We need to find \( s \) such that:
    \[ s^3 = 125 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{125} \]

    We know that:
    \[ 5^3 = 125 \]

    Therefore:
    \[ s = 5 \]

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: A roller skater is skating in a skatepark modeled as a perfect cube. The volume of the skatepark, in cubic meters, is 343. What is the length of the edges of the skatepark in meters?

GPT-4o:

    To find the length of the edges of the skatepark, we need to determine the side length of the cube. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the side length of the cube. Given that the volume \( V \) is 343 cubic meters, we can set up the equation:

    \[ s^3 = 343 \]

    To find \( s \), we take the cube root of both sides of the equation:

    \[ s = \sqrt[3]{343} \]

    We know that:

    \[ 7 \times 7 \times 7 = 343 \]

    Thus:

    \[ \sqrt[3]{343} = 7 \]

    So, the length of the edges of the skatepark is 7 meters.

    ### Answer: 7 meters

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: An ice skate manufacturer has a design for cubical boxes to package a pair of skates. If the volume of this box is 1 cubic foot, what is the length of a side of this box in feet?

GPT-4o:

    To find the length of a side of the cubical box, we need to determine the cube root of the volume. The volume of a cube is given by the formula:

    \[ V = s^3 \]

    where \( V \) is the volume and \( s \) is the length of a side.

    Given that the volume \( V \) is 1 cubic foot, we have:

    \[ 1 = s^3 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{1} \]

    Since the cube root of 1 is 1, we get:

    \[ s = 1 \]

    ### Answer: 1 foot

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: In a video game, a player notices that a treasure chest contains an item cube with a volume of 729 cubic units. What is the length of each side of the item cube?

GPT-4o:

    To find the length of each side of the item cube, we need to determine the cube root of the volume. The volume of a cube is given by \( V = s^3 \), where \( s \) is the length of a side.

    Given:
    \[ V = 729 \]

    We need to find \( s \) such that:
    \[ s^3 = 729 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{729} \]

    We know that:
    \[ 9 \times 9 \times 9 = 729 \]

    Therefore:
    \[ \sqrt[3]{729} = 9 \]

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: A cookie dough is kneaded into a cube shape before baking. If the dough has a volume of 512 cubic cm, what is the length of each side of the cube in cm?

GPT-4o:

    To find the length of each side of the cube, we need to determine the cube root of the volume. The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of each side.

    Given:
    \[ V = 512 \, \text{cubic cm} \]

    We need to find \( s \) such that:
    \[ s^3 = 512 \]

    Taking the cube root of both sides:
    \[ s = \sqrt[3]{512} \]

    Calculating the cube root:
    \[ \sqrt[3]{512} = 8 \]

    Thus, the length of each side of the cube is 8 cm.

    ### Answer: 8 cm

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A tree has a cubical hole in its trunk. The volume of the cubical hole is 8 cubic feet. What is the length of the edge of this cubic hole in feet?

GPT-4o:

    To find the length of the edge of the cubical hole, we need to determine the side length of a cube whose volume is 8 cubic feet. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the length of the edge of the cube. We are given that the volume \( V \) is 8 cubic feet. Therefore, we need to solve for \( s \) in the equation:

    \[ s^3 = 8 \]

    To find \( s \), we take the cube root of both sides of the equation:

    \[ s = \sqrt[3]{8} \]

    The cube root of 8 is 2, because:

    \[ 2^3 = 2 \times 2 \times 2 = 8 \]

    Thus, the length of the edge of the cubical hole is 2 feet.

    ### Answer: 2 feet

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A guitarist uses a particular type of guitar string. The thickness of the string, in hundreds of a millimeter, cubed, will determine the pitch of a certain note, the guitarist wishes to play. If he needs the pitch to equal 343 Hz, what is the thickness of the string he should choose?

GPT-4o:

    To determine the thickness of the guitar string, we need to solve for the thickness \( t \) given that the pitch is equal to 343 Hz. The relationship between the thickness and the pitch is given by:

    \[ t^3 = 343 \]

    To find \( t \), we need to take the cube root of 343:

    \[ t = \sqrt[3]{343} \]

    We know that:

    \[ 343 = 7^3 \]

    Therefore:

    \[ \sqrt[3]{343} = \sqrt[3]{7^3} = 7 \]

    So, the thickness of the string should be 7 hundredths of a millimeter.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: The cubic area of the compass box is 729 cubic cm. What is the length of one edge of this cubical compass box, given that it is a cube?

GPT-4o:

    To find the length of one edge of a cubical box, we need to determine the cube root of the volume. The volume of the cube is given as 729 cubic cm.

    The formula for the volume of a cube is:
    \[ V = a^3 \]
    where \( V \) is the volume and \( a \) is the length of one edge.

    Given:
    \[ V = 729 \, \text{cubic cm} \]

    We need to find \( a \) such that:
    \[ a^3 = 729 \]

    To find \( a \), we take the cube root of 729:
    \[ a = \sqrt[3]{729} \]

    Calculating the cube root:
    \[ \sqrt[3]{729} = 9 \]

    Therefore, the length of one edge of the cubical compass box is 9 cm.

    ### Answer: 9 cm

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: A book is written with a unique style where every page is in the shape of a cube. If the volume of one page is 64 cubic inches, what is the side length of each page?

GPT-4o:

    To find the side length of each page, we need to determine the side length of a cube with a volume of 64 cubic inches. The volume \( V \) of a cube is given by the formula:

    \[ V = s^3 \]

    where \( s \) is the side length of the cube. We are given that \( V = 64 \) cubic inches. Therefore, we need to solve for \( s \) in the equation:

    \[ s^3 = 64 \]

    To find \( s \), we take the cube root of both sides:

    \[ s = \sqrt[3]{64} \]

    We know that:

    \[ 4 \times 4 \times 4 = 64 \]

    Thus,

    \[ \sqrt[3]{64} = 4 \]

    So, the side length of each page is 4 inches.

    ### Answer: 4 inches

Expected answer: 4

Correct? Yes