Let's say that we want to find the volume of a sphere of radius
using volumes of revolution.
We know that the equation of a circle of radius
centered at the origin is

The upper half semicircle is given by
Now, we want to rotate the upper half semicircle around the
-axis. This will give us a sphere of radius
We use the washer/disk method to find the volume of the sphere. The volume of the sphere is
Hence, the volume of a sphere of radius
is
