Volume of Prisms and Cylinders

Once one understands how to find the volume of a prism, the derivation of the volume of a cylinder is fairly trivial. Cylinders are, essentially, just prisms with a circular base, so finding the volume of a cylinder is just like finding the volume of a cylinder.

The formula for the volume of a prism is V = B * h, where V is volume, B is the area of the base, and h is the height of the prism. The base of a cylinder is a circle, which has area πr². Height, obviously, is the same in a cylinder as it is in a prism. By substituting πr² for B in the formula for the volume of a prism, we arrive at the formula for the volume of a cylinder:

V = πr²h.