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