### Home > CALC > Chapter 8 > Lesson 8.1.6 > Problem8-61

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 $\frac { 4 } { 3 }π r^3$.

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.