Volume of Cylinder

Theorem

The volume $V_C$ of a cylinder whose base is of area $A$ and whose height is $h$ is given by:

$V_C = A h$

Proof

Consider a cylinder $C$ whose base is of area $A$ and whose height is $h$.

Consider a cuboid $K$ whose height is $h$ and whose base is also $A$.

Let $C$ 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.

From Volume of Cuboid, $K$ has volume given by:

$V_K = A h$

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cylinder
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cylinder