The volume $V_C$ of a cylinder whose bases are circles of radius $r$ and whose height is $h$ is given by the formula:
Consider a cylinder $C$ whose base is a circle of radius $r$ and whose height is $h$.
Consider a cuboid $K$ whose height is $h$ and whose base has the same area as the base of $C$.
Let the area of those bases be $A$.
Let the cylinder $C$ be positioned with its base in the same plane as the base of $K$.
By Cavalieri's Principle $C$ and $K$ have the same volume.
The bases of $C$ are circles of radius $r$.
From Area of Circle, the area of each base therefore gives:
From Volume of Cuboid, $K$ has volume given by:
Hence the result.