How to calculate volume — cuboid, cube and cylinder
How do you calculate volume?
Volume measures how much space a solid takes up — how many one-centimetre cubes would fit inside it. Every familiar solid has a short formula: for a cuboid multiply length by width by height, for a cube one edge is enough, and for a cylinder you work with the area of the circular base. We calculate all of them together, including the useful conversion to litres.
Worked examples, step by step
What is the volume of a cuboid 5 cm long, 4 cm wide and 3 cm high?
- The formula: volume = length × width × height
- Substitute: 5 × 4 × 3
- Calculate: 5 × 4 = 20, then 20 × 3 = 60
- Answer: 60 cm³ (cubic centimetres)
What is the volume of a cube with edges of 6 cm?
- In a cube all three dimensions are equal, so volume = edge × edge × edge
- Substitute: 6 × 6 × 6
- Calculate: 6 × 6 = 36, then 36 × 6 = 216
- Answer: 216 cm³
What is the volume of a cylinder with base radius 3 cm and height 10 cm? (Take π ≈ 3.14.)
- The formula: volume of a cylinder = area of the base × height, that is π × radius × radius × height
- Area of the base: 3.14 × 3 × 3 = 28.26 cm²
- Multiply by the height: 28.26 × 10 = 282.6
- Answer: about 282.6 cm³
A fish tank is a cuboid 40 cm long, 25 cm wide and 30 cm high. How many litres of water does it hold?
- Work out the volume in cm³: 40 × 25 × 30 = 30 000 cm³
- Remember: 1 litre = 1000 cm³
- Convert: 30 000 ÷ 1000 = 30
- Answer: the tank holds 30 litres
Now try it yourself
Frequently asked questions
What is the difference between volume and surface area?
Volume measures how much fits inside the solid (cubic units — cm³); surface area measures the total area of the faces on the outside (square units — cm²). For the cuboid in the example the volume is 60 cm³ and the surface area is 94 cm².
What units is volume measured in?
Cubic centimetres (cm³), cubic metres (m³) — and for liquids, litres and millilitres. Useful to remember: 1 millilitre = 1 cm³, and 1 litre = 1000 cm³.
How do you measure the volume of an irregular object, such as a stone?
By displacement: put the object into a measuring jug of water and see how much the water level rises. The rise in volume is exactly the volume of the object.
How do you calculate the volume of a pyramid or a cone?
For both, the volume is a third of what the "full" solid with the same base and height would have: volume = area of the base × height ÷ 3. The cone formula is on the GCSE formulae sheet.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: