Volume of a Cylinder Formula with Worked Examples

The volume of a cylinder formula is V = πr²h: find the area of the circular base (πr²) and multiply it by the height. Below are three fully worked examples, from the easy case to working backwards.

What the formula means

• V is the volume: how much space is inside, in cubic units (cm³, m³).
• r is the radius of the circular base.
• h is the height: the straight distance between the two circles.
• πr² is the area of the base, so the formula is simply base area × height.

Example 1: radius and height given

A cylinder has a radius of 3 cm and a height of 7 cm. Find its volume.

• V = πr²h
• V = π × 3² × 7
• V = π × 9 × 7 = π × 63
• V = 197.92 cm³

Example 2: diameter given

A can is 10 cm across and 12 cm tall. How much does it hold?

• Radius = 10 ÷ 2 = 5 cm
• V = π × 5² × 12
• V = π × 25 × 12 = π × 300
• V = 942.48 cm³ (about 0.94 litres, because 1,000 cm³ = 1 litre)

Example 3: find the height from the volume

A cylinder holds 1,000 cm³ and has a radius of 5 cm. How tall is it?

• 1,000 = π × 5² × h
• 1,000 = 78.54 × h
• h = 1,000 ÷ 78.54 = 12.73 cm

Common mistakes

1. Using the diameter as the radius. Halve it first.
2. Squaring the height instead of the radius. Only r is squared.
3. Mixing units. Convert everything to the same unit before you multiply.

More cylinder formulas (surface area, curved area) and a printable sheet are on the cylinder formulas page.