Volume · Usually met around P5
Units of volume
1 m³ = 100 × 100 × 100 cm³.
How to do it
Method
1 m³ = 100 × 100 × 100 cm³
1 m³ = 1,000,000 cm³
Another way
Think of the cubes
100 along each edge: 100 × 100 × 100 cubes
In full
Small things (dice, books, boxes) are measured in cubic centimetres (cm³); big things (containers, rooms, pools) in cubic metres (m³). 1 m³ is a cube with 1 m sides: 100 cm each way, holding 100 × 100 × 100 = 1,000,000 cubes of 1 cm³, so 1 m³ = 1,000,000 cm³. To convert, m³ to cm³ is × 1,000,000 and cm³ to m³ is ÷ 1,000,000. Careful: lengths differ 100 times, areas 100 × 100 times, volumes 100 × 100 × 100 times. Tinier things (a grain of rice, a drop of water) are measured in cubic millimetres (mm³): 1 cm = 10 mm, so 1 cm³ = 10 × 10 × 10 = 1000 mm³. Huge things (lakes, mountains) are measured in cubic kilometres (km³): 1 km = 1000 m, so 1 km³ = 1000 × 1000 × 1000 = 1,000,000,000 m³.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
8,500,000 cm³ = □ m³
Show the answer and working
Answer: 8.5
Divide by 1,000,000: 8,500,000 ÷ 1,000,000 = 8.5.
Example 2
251 cm³ = □ mm³
Show the answer and working
Answer: 251000
1 cm = 10 mm, so 1 cm³ = 10 × 10 × 10 = 1000 mm³: 251 × 1000 = 251,000.
Example 3
How many 1 cm cubes fit in a cube-shaped box with 1 m sides?
- A. 10,000
- B. 100
- C. 1,000
- D. 1,000,000
Choose the right answer
Show the answer and working
Answer: D. 1,000,000
1 × 100 along each edge, three ways multiplied: 1,000,000.
Practise it in the game →Volume · Free to start, unlimited questions, no download