GEOMETRY PROOF: VOLUME OF A SPHERE
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.
r = radius of the sphere, which is a constant.
y = rotating radii, which are not constant.