Volume & Capacity
Finding the volume of cubes, cuboids and simple 3D shapes using formulae.
What is Volume & Capacity?
Volume is the amount of space inside a 3D shape. It is measured in cubic units (cm cubed, m cubed). Capacity is how much liquid a container can hold, measured in ml or litres.
In the 11+ exam, the most common volume questions involve cubes and cuboids. You may also need to count unit cubes in a 3D diagram.
Step-by-Step Method
For a cuboid: V = length x width x height
Multiply all three dimensions together.
For a cube: V = side x side x side
A cube has all sides equal, so V = s cubed.
For counting cubes, work layer by layer
Count the cubes in one layer, then multiply by the number of layers.
Link to capacity
1 cm cubed = 1 ml. So 1,000 cm cubed = 1 litre.
Use the correct units
Volume uses cubic units: cm cubed, m cubed.
Worked Examples
Find the volume of a cuboid 4cm x 3cm x 5cm.
Working
- V = l x w x h.
- V = 4 x 3 x 5 = 60 cm cubed.
Find the volume of a cube with side length 6cm.
Working
- V = s x s x s.
- V = 6 x 6 x 6 = 216 cm cubed.
A box is 5cm x 4cm x 3cm. How many 1cm cubes fit inside?
Working
- Volume of box = 5 x 4 x 3 = 60 cm cubed.
- Each small cube = 1 cm cubed.
- 60 / 1 = 60 cubes.
Common Mistakes
Confusing area (2D) and volume (3D) – only multiplying two dimensions.
Area uses 2 dimensions, volume uses 3. Make sure you multiply all three.
Using the wrong units (cm squared instead of cm cubed).
Volume is always in CUBIC units: cm cubed, m cubed, etc.
Forgetting hidden cubes in 3D diagrams.
In a stacked cube diagram, there are cubes underneath that you cannot see. Count by layers.
Top Tips
- Remember: 1 cm cubed = 1 ml. This is useful for converting between volume and capacity.
- If a question gives you volume and two dimensions, divide to find the third: h = V / (l x w).
- For cube numbers: 1 cubed = 1, 2 cubed = 8, 3 cubed = 27, 4 cubed = 64, 5 cubed = 125.
- Draw or visualise the shape to make sure you have identified all three dimensions correctly.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions