A tank is a cuboid 80 cm long, 50 cm wide and 40 cm high. How many litres of water does it hold when full?
- Volume = 80 × 50 × 40 = 160 000 cm3.
- 1 litre = 1000 cm3, so divide by 1000.
- 160 000 ÷ 1000 = 160.
Answer: 160 litres
Units of measure
Maths · Mensuration. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
The metric system works in steps of 10, 100 and 1000. To change to a smaller unit you multiply, because you need more of them. To change to a larger unit you divide.
Area and volume need extra care. There are 100 cm in 1 m, but a square metre is 100 cm by 100 cm, so it holds 100 × 100 = 10 000 cm2. A cubic metre holds 100 × 100 × 100 = 1 000 000 cm3. So you square the length factor for area and cube it for volume.
Capacity is the amount a container holds, measured in litres and millilitres. It is linked to volume: 1 ml is the same as 1 cm3.
Rules to remember
- Length: 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km
- Mass: 1000 mg = 1 g; 1000 g = 1 kg; 1000 kg = 1 tonne
- Area: 1 cm2 = 100 mm2; 1 m2 = 10 000 cm2; 1 km2 = 1 000 000 m2
- Volume: 1 cm3 = 1000 mm3; 1 m3 = 1 000 000 cm3
- Capacity: 1 litre = 1000 ml = 1000 cm3; 1 ml = 1 cm3; 1 m3 = 1000 litres
- Speed: km/h ÷ 3.6 = m/s; m/s × 3.6 = km/h (36 km/h = 10 m/s)
Common mistake
Students use 100 to change m2 to cm2, as if it were a length. Square the factor for area (× 10 000) and cube it for volume (× 1 000 000).
Worked example
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