🔗 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of the volume.
    The cube root of 512 is 8 because 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning: We need to find the cube root of 729, as the cube root of a number represents the side length of a cube with that volume. The cube root of 729 is 9, because 9 * 9 * 9 = 729.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of the volume.  The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by multiplying the length of one side by itself three times.  Therefore, to find the length of one side of a cube when you know its volume, you need to find the cube root of the volume. The cube root of 512 is 8, as 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning: Let the length of each side of the cubical mountain be x kilometers.
    The volume of a cube is calculated by x^3
    Therefore x^3 = 64 km^3
    Taking the cube root of both sides gives us x = 4 km
    ### 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?

Gemma 2B:

    Reasoning:  We need to find the cube root of 512 to determine the length of one edge. The cube root of 512 is 8, as 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning:  A cube is made up of equal sides in length, width, and height. This means the total number of blocks (343) is the result of multiplying the length of one side by itself three times (length x length x length).  We need to find what number, multiplied by itself three times, equals 343.

    That number is 7, because 7 * 7 * 7 = 343

    ### Answer: 7 blocks

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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the side length (s). This means we need to find the cube root of 512 to determine the side length.
    The cube root of 512 is 8 because 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning: Let the edge length of the cube be  'x' mm.
    The volume of a cube is calculated by the formula: Volume = x^3
    We are given that the volume of the eraser cube is 512 mm^3.
    Therefore, x^3 = 512.
    To find x, we need to find the cube root of 512.
    The cube root of 512 is 8, as 8 * 8 * 8 = 512.
    So, the edge length 'x' 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side).  Since the volume is 8 cubic cm, we need to find the cube root of 8.
    The cube root of 8 is 2, because 2*2*2 = 8
    ### 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?

Gemma 2B:

    Reasoning:  Let 's' represent the length of one edge of the cube. The volume of a cube is calculated by s³.  We need to find 's' such that s³ = 27.  The cube root of 27 is 3, as 3 * 3 * 3 = 27.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of the volume. The cube root of 1 is 1, as 1*1*1=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?

Gemma 2B:

    Reasoning: The flower holds 125 milliliters of nectar, which means its volume is 125 cubic centimeters.
    Since the flower is a cube, we need to find the cube root of 125 to find the length of one side.
    The cube root of 125 is 5, as 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides (s*s*s or s^3).  Therefore, to find the side length we need to find the cube root of 125. The cube root of 125 is 5, because 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its edges. Therefore, to find the length of an edge, we need to find the cube root of the volume.  The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Since the volume is 1 cubic cm, we need to find the cube root of 1.
    The cube root of 1 is 1, as 1 * 1 * 1 = 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?

Gemma 2B:

    Reasoning: To find the length of one edge of a cube, we need to find the cube root of its volume.  The cube root of 216 is 6, because 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the side length.  Therefore, to find the side length, we need to find the cube root of the volume. The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.
    ### 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?

Gemma 2B:

    Reasoning: We need to find the cube root of 125, as the volume of a cube is calculated by side * side * side.
    The cube root of 125 is 5, because 5 * 5 * 5 = 125.
    ### Answer: 5 centimeters.

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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side).  We need to find the number that, when cubed, equals 125.
    5 * 5 * 5 = 125
    ### Answer: 5 centimeters

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?

Gemma 2B:

    Reasoning: Let the length of one side of the building be x meters.
    The volume of a cuboid is given by length * width * height.
    Since all sides are equal, the volume of the building is x * x * x = x³ cubic meters.
    We are given that the volume is 216 cubic meters.
    Therefore, x³ = 216.
    Taking the cube root of both sides, we get x = 6 meters.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side). To find the side length, we need to find the cube root of the volume.
    The cube root of 343 is 7 because 7 * 7 * 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by the following formula: V = s^3, where V is the volume, and s is the length of a side.  We are given that V = 729, so we need to find the cube root of 729 to determine the length of a side.  The cube root of 729 is 9, since 9 * 9 * 9 = 729
    ### Answer: 9

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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its edges.  Therefore, the length of one edge is the cube root of the volume.  The cube root of 8 is 2, since 2*2*2 = 8.
    ### 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?

Gemma 2B:

    Reasoning:  A cube has equal length, width, and height. To find the length of one side, we need to find the cube root of the volume.  The cube root of 343 is 7, because 7 * 7 * 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its edges. Therefore, to find the length of the edge, we need to find the cube root of the volume.  The cube root of 8 is 2, as 2 * 2 * 2 = 8.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by calculating (side length) * (side length) * (side length).  So to find the side length from the volume, we need to find the cube root of 729. The cube root of 729 is 9, because 9 * 9 * 9 = 729.
    ### 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?

Gemma 2B:

    Reasoning: Let the length of one side of the cuboid be  'x' feet.
    The volume of a cuboid is given by length * width * height.
    Since all sides are equal, the volume is x * x * x = x³ cubic feet.
    We are given that the volume is 1000 cubic feet. So, x³ = 1000
    Taking the cube root of both sides, we get x = 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?

Gemma 2B:

    Reasoning: We need to find the number that, when multiplied by itself three times (cubed), equals 512.
    Let's try some numbers:
    *  7 x 7 x 7 = 343 (too small)
    *  8 x 8 x 8 = 512 (This is it!)

    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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its edges (side * side * side).  We need to find the number that, when multiplied by itself three times, equals 27.

    Since 3 * 3 * 3 = 27, the length of one edge of the inflated hat 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?

Gemma 2B:

    Reasoning:  We need to find the number that, when multiplied by itself three times (since it's a cube), equals 27. This is the cube root of 27.
    The cube root of 27 is 3, as 3 * 3 * 3 = 27.

    ### Answer: 3 grapes.

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?

Gemma 2B:

    Reasoning: We need to find the cube root of the volume to determine the side length.  The cube root of 216 is the number that, when multiplied by itself three times, equals 216.
    Since 6 * 6 * 6 = 216, the cube root of 216 is 6.

    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its edges (side * side * side). To find the length of an edge, we need to find the cube root of the volume.
    The cube root of 64 is 4, as 4 * 4 * 4 = 64.
    ### Answer: 4 millimeters

Expected answer: 4

Correct? Yes

🔗 Problem

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

Gemma 2B:

    Reasoning: To find the original number, we need to find the cube root of 64, which is the number that, when multiplied by itself three times, equals 64.
    The cube root of 64 is 4 because 4 * 4 * 4 = 64.
    ### 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?

Gemma 2B:

    Reasoning:  A liter is the same as a cubic decimeter (dm³). If the mug holds 1 liter, it has a volume of 1 cubic decimeter.
    Since the mug is a cube, all its sides are equal in length.
    Therefore, each side of the mug is 1 decimeter long.
    A decimeter (dm) is equal to 0.1 meters (m).

    ### Answer: 0.1 liters

Expected answer: 1

Correct? No

🔗 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the side length (sxsxs = Volume).  Therefore, we need to find the cube root of 343 to determine the side length.  The cube root of 343 is 7, as 7 x 7 x 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning: To find the length of one side of the smaller cube, we need to find the cube root of the larger cube's volume. This is because the volume of a cube is found by cubing the side length (side * side * side).
    The cube root of 729 is 9, because 9 * 9 * 9 = 729
    ### Answer: 9 cm

Expected answer: 9

Correct? Yes

🔗 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?

Gemma 2B:

    Reasoning:  We need to find the cube root of 216, which means finding a number that, when multiplied by itself three times, equals 216.
    Since 6 * 6 * 6 = 216, the cube root of 216 is 6.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the side length.  Therefore, the side length of a cube is found by taking the cube root of the volume.
    The cube root of 216 is 6 because 6*6*6 = 216.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the side length (sxsxs = Volume).  Therefore,  the side length of a cube is found by taking the cube root of the volume.  The cube root of 27 is 3, because 3x3x3 = 27.
    ### Answer: 3 centimeters.

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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side). Therefore, to find the side length, we need to find the cube root of the volume. The cube root of 27 is 3, as 3 * 3 * 3 = 27.
    ### 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?

Gemma 2B:

    Reasoning:  A cube has all sides equal. To find the length of one side of a cube given its volume, you need to find the cube root of the volume. The cube root of 216 is 6, because 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one side (side * side * side).  To find the side length, we need to find the cube root of the volume. The cube root of 216 is 6, because 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one of its edges (side * side * side). To find the length of one edge, we need to find the cube root of the volume.
    The cube root of 125 is 5, as 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning:  To find the length of each side of a cube when you know the total number of items (flowers in this case) arranged in a cube, you need to find the cube root. The cube root of a number is the value that, when multiplied by itself three times, equals the original number.
    The cube root of 125 is 5, because 5 * 5 * 5 = 125.

    ### 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?

Gemma 2B:

    Reasoning:  We need to find the cube root of 1000, meaning finding the number that, when multiplied by itself three times, equals 1000.
    The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.
    ### Answer: 10 centimeters

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?

Gemma 2B:

    Reasoning: Let $x$ be the length of one side of the cargo hold.  Since it is a cube, its volume is $x^3$, and we have the equation $x^3 = 27$.  Taking the cube root of both sides, we get $x = \sqrt[3]{27}$.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one of its sides (side * side * side). To find the side length, we need to find the cube root of the volume. The cube root of 216 is 6, as 6 * 6 * 6 = 216.
    ### Answer: 6 centimeters.

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)?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its edges.  Therefore, to find the length of one edge of the box, we need to find the cube root of 729. The cube root of 729 is 9 because 9*9*9 = 729.
    ### 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.)

Gemma 2B:

    Reasoning: We need to find the cube root of 27 to determine the letter's position in the alphabet.
    The cube root of 27 is 3 because 3 * 3 * 3 = 27.
    The letter corresponding to the 3rd position in 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of the volume.  The cube root of 1 is 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?

Gemma 2B:

    I cannot answer this question. The provided context mentions that the temperature at the heart of the object is directly proportional to the cube of its length, but it does not specify the proportionality constant or provide a baseline temperature for a known length.

Expected answer: 9

Correct? No

🔗 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side).
    To find the side length, we need to find the cube root of the volume.
    The cube root of 8 is 2, because 2 * 2 * 2 = 8.
    ### Answer: 2 centimeters

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?

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one of its edges. Therefore, to find the length of one edge, we need to find the cube root of the volume.  The cube root of 729 is 9, because 9 * 9 * 9 = 729.
    ### Answer: 9 centimeters.

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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides (s*s*s or s³).  Therefore, to find the side length, we need to find the cube root of the volume. The cube root of 125 is 5, because 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides.  Therefore, the length of one side of the box is the cube root of 343 cubic inches. The cube root of 343 is 7, because 7*7*7=343.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by the formula V = a³, where 'a' is the length of an edge and 'V' is the volume. We know that the volume (V) is 512 cubic centimeters. To find the length of an edge, we need to find the cube root of the volume. The cube root of 512 is 8, as 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the side length (s^3).  To find the side length from the volume, we need to find the cube root of 512.
    The cube root of 512 is 8, as 8 * 8 * 8 = 512
    ### 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?

Gemma 2B:

    Reasoning: To find the length of one edge of a cube, we need to find the cube root of its volume.
    The cube root of 729 is 9, because 9 * 9 * 9 = 729.
    ### Answer: 9 centimeters.

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)?

Gemma 2B:

    Reasoning: We need to find the cube root of 8 to find the length of one edge because the volume of a cube is found by cubing the length of one edge.
    The cube root of 8 is 2 because 2*2*2 = 8
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (side * side * side).  Since the dolphin's call fills 1 unit^3, we need to find the cube root of 1.
    The cube root of 1 is 1, as 1 * 1 * 1 = 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Therefore, to find the side length of a cube with a given volume, we need to calculate the cube root of the volume.

    The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.

    ### Answer: 10 mm.

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?

Gemma 2B:

    Reasoning: The volume of a cube is found by multiplying the length, width, and height. Since it's a cube, all sides are equal. We need to find a number that, when multiplied by itself three times (cubed), equals 1.
    1 x 1 x 1 = 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?

Gemma 2B:

    Reasoning: We need to find the cube root of 216 to determine the side length of the cube-shaped box.  The cube root of 216 is 6 because 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of 64.  The cube root of 64 is 4 because 4 * 4 * 4 = 64.
    ### 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?

Gemma 2B:

    Reasoning:  Let the length of the edge of the cubical toothbrush holder be x cm.
    The volume of the cubical toothbrush holder = x*x*x cubic centimeters.
    Thus, x*x*x = 1000 i.e. x^3 = 1000.
    So, x = 10 as 10*10*10 = 1000.
    ### Answer: 10 centimeters

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?

Gemma 2B:

    Reasoning:  The volume (V) of a cube is calculated by cubing the side length (f): V = f³.
    We know the volume of the cube-shaped oven is 125 cubic inches, so 125 = f³.
    To find the side length (f), we need to find the cube root of 125, which is 5 because 5 * 5 * 5 = 125.
    Therefore, the length of each side of the loaf is 5 inches.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the side length (s*s*s or s^3).  We know the volume is 64, so we need to find the cube root of 64, which is the number that multiplied by itself three times equals 64.
    The cube root of 64 is 4, because 4*4*4 = 64
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of 216.  The cube root of 216 is 6 because 6 * 6 * 6 = 216.
    ### 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.

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one edge (s), meaning V=s³. We are given that the volume (V) is 512 cubic inches. To find the length of one edge (s), we need to find the cube root of the volume.

    The cube root of 512 is 8, as 8 * 8 * 8 = 512.

    ### 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?

Gemma 2B:

    Reasoning:  A cubical arrangement means the eggs form a perfect cube. To find the length of an edge, we need to find the cube root of the total number of eggs. The cube root of 27 is 3, as 3 * 3 * 3 = 27.

    ### 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'?

Gemma 2B:

    Reasoning: Let the length of one edge of the cube be x meters.  The volume of the cube is then x*x*x = 512 cubic meters. We need to find the cube root of 512, that is, find x such that x^3=512. Since 8*8*8=512, the cube root of 512 is 8.
    ### 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?

Gemma 2B:

    Reasoning: To find the length of one edge of a cube from its volume, we need to find the cube root of the volume.  The cube root of 343 is 7, since 7 * 7 * 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning:  To find the side length of a cube given its volume, we need to find the cube root of the volume. The cube root of 343 is 7, because 7 * 7 * 7 = 343.
    ### Answer: 7 centimeters.

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?

Gemma 2B:

    Reasoning: We need to find the cube root of 216 because the cube root of a number represents the side length of a cube with that volume.
    The cube root of 216 is 6, since 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning: To find the side length of a cube given its volume, we need to find the cube root of the volume. The cube root of 343 is 7, because 7 * 7 * 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning: To find the length of one side of a cube, we need to find the cube root of the volume.
    The cube root of 216 is 6, because 6 * 6 * 6 = 216.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides. Therefore, to find the side length, we need to find the cube root of the volume. The cube root of 1 cubic meter is 1 meter.
    ### 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?

Gemma 2B:

    Reasoning: We need to find the cube root of 1000, as the cube root of a number gives us the side length of a cube with that volume.
    The cube root of 1000 is 10, because 10 * 10 * 10 = 1000.
    ### Answer: 10 centimeters

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?

Gemma 2B:

    Reasoning: To find the length of one side of a cube, we need to find the cube root of its volume.  The cube root of 512 is 8, because 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides. Therefore, to find the side length, we need to find the cube root of the volume.  The cube root of 64 is 4, because 4 * 4 * 4 = 64.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides.  Therefore, to find the side length, we need to find the cube root of 27. The cube root of 27 is 3, as 3 * 3 * 3 = 27.
    ### 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?

Gemma 2B:

    Reasoning: Let the length of the sides be $x$. The volume of the cargo space is $x\cdot x\cdot x = 8$ cubic meters. We need to find the cube root of 8.
    The cube root of 8 is 2 because  $2\cdot2\cdot2 = 8$.
    ### 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?

Gemma 2B:

    Reasoning:  We need to find the cube root of 343, as this represents the volume of a cube. The cube root of 343 is 7, since 7 * 7 * 7 = 343.
    ### Answer: 7 grapes

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?

Gemma 2B:

    Reasoning: To find the length of a side of a cube, we need to find the cube root of the volume.
    The cube root of 343 is 7, because 7 * 7 * 7 = 343.
    ### 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.

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its edges. Therefore, to find the length of an edge, we need to find the cube root of the volume. The cube root of 27 is 3, as 3 * 3 * 3 = 27.
    ### Answer: 3 centimeters.

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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by the formula V = s^3, where V is the volume and s is the edge length. We know the volume (V) is 8 km^3. To find the edge length (s), we need to find the cube root of the volume.
    The cube root of 8 is 2, as 2 * 2 * 2 = 8.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one of its sides (side * side * side). To find the side length, we need to find the cube root of the volume.  The cube root of 125 is 5, because 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides (side * side * side).  To find the side length when you know the volume, you need to find the cube root of the volume. The cube root of 64 is 4, because 4 * 4 * 4 = 64.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is found by cubing the length of one of its sides.  Therefore, we need to find the cube root of 125 to determine the side length of the treasure chest.
    The cube root of 125 is 5, because 5 * 5 * 5 = 125.
    ### 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?

Gemma 2B:

    Reasoning: A cube has all sides equal, and the volume of a cube is found by cubing the side length. So, to find the side length, we need to find the cube root of 1 cubic meter.
    The cube root of 1 is 1, as 1*1*1 = 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its sides (s). We know the volume is 125 cubic centimeters (V = 125 cm³), so we need to find the cube root of the volume to determine the side length.

     V = s³
     125 cm³ = s³
     ∛125 cm³ = s
     5 cm = s

     Therefore, the length of one side of this cheese cube is 5 centimeters.
     ### Answer: 5 centimeters.

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?

Gemma 2B:

    Reasoning:  We need to find the cube root of 343, since the volume of a cube is found by cubing the side length. 7 * 7 * 7 = 343.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the side length. Since the volume of the box is 1 cubic foot, we need to find the cube root of 1. The cube root of 1 is 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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one of its sides (since all sides are equal).  Therefore, to find the side length, we need to find the cube root of 729. The cube root of 729 is 9, as 9 * 9 * 9 = 729.

    ### Answer: 9 units

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?

Gemma 2B:

    Reasoning:  The volume of a cube is found by cubing the length of one side (side * side * side).  To find the side length when you know the volume, you need to find the cube root of the volume.  The cube root of 512 is 8, because 8 * 8 * 8 = 512.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by cubing the length of one of its edges.  Therefore, to find the edge length, we need to find the cube root of the volume. The cube root of 8 is 2, because 2 * 2 * 2 = 8.
    ### 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?

Gemma 2B:

    I can't answer the question. The provided context mentions the relationship between string thickness and pitch, but doesn't give a mathematical formula to calculate the exact thickness needed for a 343 Hz pitch.
    ### Answer: Not enough information.

Expected answer: 7

Correct? No

🔗 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?

Gemma 2B:

    Reasoning:  The volume of a cube is calculated by cubing the length of one of its edges.  To find the length of one edge, we need to find the cube root of the volume. The cube root of 729 is 9, because 9 * 9 * 9 = 729.
    ### 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?

Gemma 2B:

    Reasoning: The volume of a cube is calculated by the formula V = s³, where 's' is the side length. We know V (volume) is 64 cubic inches. To find 's', we need to find the cube root of 64.  The cube root of 64 is 4, as 4 * 4 * 4 = 64.
    ### Answer: 4 inches

Expected answer: 4

Correct? Yes