{"knowledge_schema": {"broad_category": "Mathematics \u2192 Differential Geometry \u2192 Area Calculation", "refinement": "This problem involves calculating the area of a surface defined by a specific metric, which in this case is a pseudosphere.", "specific_scope": "The focus is on determining the area of a pseudosphere with a given radius using the provided metric formula.", "goal": "Calculate the area of the pseudosphere of radius r = 3 based on the given metric."}, "summary": "This problem is rooted in differential geometry, specifically in calculating the area of a surface defined by a metric. The metric provided describes a pseudosphere, and the task is to find the area for a specific radius. The area calculation reveals that the area of the pseudosphere of radius r = 3 is infinite, indicating that the surface extends indefinitely in certain directions. Thus, the answer to the question is +\u221e."}