Volume of Right Circular Cylinder/Proof 1

Theorem

The volume $V_C$ of a right circular cylinder whose bases are circles of radius $r$ and whose height is $h$ is given by the formula:

$V_C = \pi r^2 h$

Proof

Consider a right circular cylinder $C$ whose base is a circle of radius $r$ and whose height is $h$.

Let $V_C$ denote the volume of $C$.

From Volume of Cylinder in terms of Height and Base Area:

$V_C = A h$

where $A$ is the area of the base of $C$.

From Area of Circle, the area of each base is:

$A = \pi r^2$

Hence:

$V_C = \pi r^2 h$

$\blacksquare$