Volume · Usually met around P5
Combined solids, and a side from a volume
Height = volume ÷ base area.
How to do it
Method
Height = volume ÷ base area
120 ÷ (6 × 5) = 4
Another way
Split and add
6 × 4 × 2 + 3 × 4 × 2 = 72
In full
A cuboid's volume = length × width × height = base area × height; a cube's = side × side × side. For a solid made of cuboids, way 1: split it into cuboids, find each volume and add; way 2: complete it to a big cuboid and take away the extra. For a side from a volume, divide backwards: height = volume ÷ (length × width) = volume ÷ base area. For a cube's side from its volume, find the number that multiplied by itself three times makes the volume: 64 = 4 × 4 × 4.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A cube's volume is 64 cm³. How many centimetres long is each side?
Show the answer and working
Answer: 4 cm
Find the number multiplied by itself three times to make 64: 4 × 4 × 4 = 64.
Example 2
A cuboid's volume is 990 cm³; it is 11 cm long and 10 cm wide. How many centimetres high is it?
Show the answer and working
Answer: 9 cm
Height = volume ÷ (length × width) = 990 ÷ 110 = 9.
Example 3
A cuboid's volume is 294 cm³, its length 7 cm and width 7 cm. Which working finds the height?
- A. 294 ÷ (7 + 7)
- B. 294 − 7 − 7
- C. 294 ÷ 7 × 7
- D. 294 ÷ (7 × 7)
Choose the right answer
Show the answer and working
Answer: D. 294 ÷ (7 × 7)
Height = volume ÷ base area = 294 ÷ (7 × 7) = 6.
Practise it in the game →Volume · Free to start, unlimited questions, no download