Stage 11 · Shape & space
Volume
Length × width × height: easy pair first.
How to do it
Method
Length × width × height: easy pair first
5 × 7 × 4: 5 × 4 = 20, 20 × 7 = 140
Another way
Length × width × height
5 × 7 = 35, 35 × 4 = 140
In full
A cuboid's volume = length × width × height; a cube's = edge × edge × edge, in cm³ or m³. Quicker: of the three numbers, multiply the easy pair first: 5 × 7 × 4 → 5 × 4 = 20, 20 × 7 = 140 cm³. Counting small cubes: one layer is length × width cubes, then times the layers: one layer is 4 × 3 = 12, there are 3 layers, 12 × 3 = 36 cubes, so 36 cm³ (count the hidden cubes too). Or work out length × width × height in order: 5 × 7 = 35, 35 × 4 = 140 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Volume of the cube = ? cm³
Show the answer and working
Answer: Volume of the cube = 27 cm³
A cube's volume is edge × edge × edge: 3 × 3 = 9, 9 × 3 = 27, so 27 cm³
Example 2
Volume of the cuboid = ? cm³
Show the answer and working
Answer: Volume of the cuboid = 150 cm³
A cuboid's volume is length × width × height: 3 × 10 = 30, 30 × 5 = 150, so 150 cm³
Example 3
Volume of the solid = ? cm³
Show the answer and working
Answer: Volume of the solid = 18 cm³
One layer is 3 × 3 = 9 small cubes, and there are 2 layers: 9 × 2 = 18 (count the hidden ones too), so 18 cm³
Example 4
Volume of the solid = ? cm³
Show the answer and working
Answer: Volume of the solid = 18 cm³
One layer is 2 × 3 = 6 small cubes, and there are 3 layers: 6 × 3 = 18 (count the hidden ones too), so 18 cm³
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