Calculus

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Intersection of a paraboloid and hemisphere.

Intersection of a paraboloid and a hemisphere in 3D, with transparent blue and pink surfaces representing the paraboloid and hemisphere, respectively. The shared region is marked by a closed curve where both surfaces meet at z = 2.

This diagram illustrates the intersection between a paraboloid and a hemisphere in 3D space. Two surfaces—the upward-facing paraboloid z = 4−x2−y2 and the hemisphere x2+y2+z2 = 6 overlap to form a shared region, labeled here with W. The image emphasizes the boundary between these surfaces through transparent rendering, helping visualize how they intersect.

This illustration is useful for multivariable calculus textbooks and analytic geometry learning materials.

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