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8-61.
  1. GEOMETRY PROOF: VOLUME OF A SPHERE

  2. Another way to view a sphere is as a semi-circle rotated about an axis. Use a generic semi-circle such as to prove that the volume of a sphere with radius r is π r3. Homework Help ✎

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

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