Volume of a Sphere

Let's say that we want to find the volume of a sphere of radius $r$ using volumes of revolution.

We know that the equation of a circle of radius $r$ centered at the origin is

$x^{2}+y^{2}=r^{2}.$

The upper half semicircle is given by: $y={\sqrt {r^{2}-x^{2}}}.$

(insert picture of semicircle)

Now, we want to rotate the upper half semicircle around the $x$-axis. This will give us a sphere of radius $r.$

(insert pictures)