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8-62.

GEOMETRY PROOF: VOLUME OF A SPHERE

Another way to view a sphere is as a semicircle rotated about an axis. Use a generic semicircle such as  to prove that the volume of a sphere with radius is . Homework Help ✎

Set up and evaluate an integral showing what happens when you rotate the arbitrary semicircle about the -axis.

Note:
 radius of the sphere, which is a constant.
rotating radii, which are not constant.