Volume of a Cylinder

A cylinder is a circle carried straight upwards. Its volume is the area of the base multiplied by the height, and since the base is a circle of radius $r$, that area is $\pi r^2$.

• $V$ — the volume
• $r$ — the radius of the base
• $h$ — the height
• $\pi$ — pi

Example

With the defaults, a radius of $r = 3$ and a height of $h = 7$. The base area is $\pi \times 3^2 = 9\pi \approx 28.2743$, so

The volume is about 197.9203.

Why base area times height

Imagine stacking thin discs, each a copy of the base, until the pile reaches the height $h$. One disc covers $\pi r^2$, and the stack is $h$ tall, so the volume is $\pi r^2 h$. The same argument works for any prism: volume equals base area times height.

Watch out

The height is measured perpendicular to the base. Enter the radius, not the diameter: a cylinder 6 across has radius 3. Doubling the radius makes the volume four times larger, whereas doubling the height only doubles it, because the radius enters squared. A cone with the same base and height holds exactly one third as much.