Converting units of volume

The two cubes have the same .

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 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, \(1~\text{cm}^3 = 1,000~\text{mm}^3\)

Here is a 10 cm cube.

A 3D cube with sides that measure 10 cm.

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 ≈ 4.5 litres

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.

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Units of measure - OCRConverting units of volume