Converting units of volume
The two cubes have the same The volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml..
Cube 1
Volume = \(1~\text{m} \times 1~\text{m} \times 1~\text{m}\)
Volume = 1 m3
Cube 2
Volume = \(100~\text{cm} \times 100~\text{cm} \times 100~\text{cm}\)
Volume = 1,000,000 cm3
Since Cube 1 and Cube 2 have the same volume, \(1~\text{m}^3 = 1,000,000 ~\text{cm}^3\)
The same method can be used to convert cm3 into mm3.
Cube 3
Volume = \(1~\text{cm} \times 1~\text{cm} \times 1~\text{cm}\)
Volume = 1 cm3
Cube 4
Volume = \(10~\text{mm} \times 10~\text{mm} \times 10~\text{mm}\)
Volume = 1,000 mm3
Since Cube 3 and Cube 4 have the same volume, \(1~\text{cm}^3 = 1,000~\text{mm}^3\)
Here is a 10 cm cube.
The volume of this cube is \(10~\text{cm} \times 10~\text{cm} \times 10~\text{cm} = 1,000~\text{cm}^3\). This volume is more usually referred to as 1 litre (1l). This means that 1ml is the same as 1 cm3.
It can be hard to visualise the size of 1 litre. Try to remember that a small bottle of water is about \(\frac{1}{3}\) litre.
The most common metric unit conversions for volume are:
- 1 m3 = 1,000,000 cm3
- 1 cm3 = 1,000 mm3
- 1 l (litre) = 1,000 ml = 1000 cm3
Example
Convert 25,000 cm3 into (a) m3 and (b) litres.
(a) 1 m3 = 100 cm x 100 cm x 100 cm = 1,000,000 cm3
\(25,000 \div 1,000,000 = 0.025~\text{m}^\text{3}\)
(b) 1l = 1000 cm3
\(25,000 \div 1,000 = 25~\text{l}.\)
Converting imperial units of volume
Imperial to metric conversions will usually be given to you in the exam but you should try to learn approximate equivalents.
A common approximate conversion for volume is:
1 gallon 鈮 4.5 litres
Example
Convert 7.5 gallons into litres.
4.5 litres 鈮 1 gallon
\(7.5 \times 4.5 \approx 33.75~\text{litres}\)
7.5 gallons is approximately 33.75 litres.