### Home > CALC > Chapter 8 > Lesson 8.1.6 > Problem 8-61

8-61.

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 r*^{3}. 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.