Example 1
Find the volume of a cuboid 5 cm long, 3 cm wide and 2 cm high.
- For a cuboid, volume = length × width × height.
- Multiply 5 × 3 × 2
- 5 × 3 × 2 = 30
So: The volume is 30 cm³.
Back to National 4
Topic
Volume
Volume measures the space inside a 3D shape. Capacity is the amount a container can hold.
Topic explanation
Volume is measured in cubic units such as cm³ because it counts cubes filling a space
For any prism, first find the area of the cross-section, then multiply by the length of the prism.
Capacity conversions often connect volume to litres. A volume of 1000 cm³ holds 1 litre
Quick methods
- Cuboid
- Volume = length × width × height
- Cube
- Multiply the side length by itself three times.
- Prism
- Volume = cross-sectional area × length
- Capacity
- 1000 cm³ = 1 litre
Worked examples
Example 2
A container holds 2500 cm³. How many litres is this?
- 1000 cm³ is 1 litre
- Divide by 1000 to change cm³ into litres
- 2500 divided by 1000 = 2.5
So: The container holds 2.5 litres.
Example 3
A triangular prism has cross-sectional area 18 cm² and length 12 cm. Find its volume.
- For a prism, volume = cross-sectional area × length.
- Use the given cross-sectional area, 18 cm².
- 18 × 12 = 216
So: The volume is 216 cm³.