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Volume of a cylinder

The area of the circular base times the height.

V = πr²h

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Volume = πr²h = 282.74
Surface area = 2πr² + 2πrh = 56.549 + 188.5 = 245.04

What the symbols mean

$V$: the volume
$r$: the radius of the circular end
$h$: the height (or length) of the cylinder

When to use it

Use it for cans, pipes, tanks, glasses and columns. For a pipe or a tube, subtract the inner cylinder from the outer one. Solve for h to see how full a cylindrical tank is from the volume poured in.

Worked example

A can has a radius of 3 cm and a height of 10 cm. What is its volume? (r = 3, h = 10)

Start from the formula.
$V = π r^{2} h$
Substitute $r$ = $3$ , $h$ = $10$ and work it out.
$V = π \cdot 3^{2} \cdot 10$
$= π \cdot 9 \cdot 10$
$\approx 282.743$

Answer V ≈ 282.74 cm³, about 283 ml

Why it works

A cylinder is a stack of identical circles. Its volume is base area times height, like any prism: $π r^{2} \times h$ .

Common mistakes

Using the diameter as r, which gives four times the volume.
Using $2πrh$ , which is the curved surface area, not the volume.