Converting units of volume

The two cubes have the same volume.

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 m³ = 1,000,000 cm³

The same method can be used to convert cm³ into mm³.

Cube 1: 1cm x 1cm x 1cm Cube 2: 10mm x 10mm x 10mm

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 cm³ = 1,000 mm³

Here is a 10 cm cube.

A 3D cube with sides that measure 10 cm.

The volume of this cube is \(10 cm \times 10 cm \times 10 cm = 1,000 cm^3\). 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) \(1~m^3 = 100~cm \times 100~cm \times 100~cm = 1,000,000~cm^3\)

\(25,000 \div 1,000,000 = 0.025~\text{m}^\text{3}\)

(b) 1 l = 1000 cm³

\(25,000 \div 1,000 = 25~l\)

Imperial units of volume

Units of volume can be converted between imperial and metric units using unit conversions. If you need to use an imperial to metric conversion in an exam, the values will be given to you.

A common conversion is:

4.5 litres ≈ 1 gallon

Example

Convert 7.5 gallons into litres.

4.5 litres ≈ 1 gallon

\(7.5 \times 4.5 \approx 33.75~\text{litres}\)

7.5 gallons is approximately 33.75 litres.

Units of measure - EdexcelConverting units of volume