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Surface area of a cylinder

Two circular ends plus the curved side, which unrolls into a rectangle.

S = 2πr² + 2πrh

Curved surface only

S_curved = 2πrh

Factorised

S = 2πr(r + h)

Calculator

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

What the symbols mean

$S$: the total surface area
$r$: the radius
$h$: the height

When to use it

Use it for the metal in a can, the label on a tin (curved part only), the paint on a tank or the insulation round a pipe. Leave out one end for an open cup, both for a tube.

Worked example

How much metal is needed for a closed can of radius 3 cm and height 10 cm? (r = 3, h = 10)

Start from the formula.
$S = 2 π r^{2} + 2 π r h$
Substitute $r$ = $3$ , $h$ = $10$ and work it out.
$S = 2 π \cdot 3^{2} + 2 π \cdot 3 \cdot 10$
$= 2 π \cdot 9 + 2 π \cdot 3 \cdot 10$
$\approx 245.044$

Answer S ≈ 245.04 cm²

Why it works

Unroll the curved side and it becomes a rectangle: its height is h and its length is the circumference $2πr$ . Add the two circles at the ends.

Common mistakes

Forgetting one or both ends, or including ends that the shape does not have.
Using $π r h$ for the curved part. The rectangle's length is the full circumference, $2πr$ .