Converting between different units | Surface area and volume of 3D objects

Surface area and volume of triangular prisms

Solving problems involving surface area, volume and capacity

17.6 Converting between different units

Surface area is measured in square units. Surface area can be expressed in square millimetres (\(\text{mm}^2\)), square centimetres (\(\text{cm}^2\)), square metres (\(\text{m}^2\)) and also square kilometres (\(\text{km}^2\)).

The diagram below shows how to convert between the different units of area.

Worked Example 17.10: Converting between units of area

Convert \(157 \text{ mm}^2\) to square centimetres.

Divide the area by \(100\).

To convert from square millimetres to square centimetres, we divide the area by \(100\):

\[\begin{align} 157 \text{ mm}^2 &= 157 \div 100 \\ &= \text{1,57} \text{ cm}^2 \end{align}\]

Worked Example 17.11: Converting between units of area

Convert \(\text{3,08} \text{ m}^2\) to square centimetres.

Multiply the area by \(100^{2}\).

To convert from square metres to square centimetres, we multiply the area by \(100^2\):

\[\begin{align} \text{3,08} \text{ m}^2 &= \text{3,08} \times \text{10 000} \\ &= \text{30 800} \text{ cm}^2 \end{align}\]

Exercise 17.1

Convert each area to square centimetres.

\(\text{2,06} \text{ m}^2\)
\(\text{7 423} \text{ mm}^2\)
\(\text{0,015} \text{ m}^2\)
\(\text{842,5} \text{ mm}^2\)
\(\text{0,416} \text{ m}^2\)

\(\text{20 600} \text{ cm}^2\)
\(\text{74,23} \text{ cm}^2\)
\(\text{150} \text{ cm}^2\)
\(\text{8,425} \text{ cm}^2\)
\(\text{4 160} \text{ cm}^2\)

Convert each area to square millimetres.

\(\text{3,4} \text{ cm}^2\)
\(\text{0,009} \text{ m}^2\)
\(\text{0,62} \text{ cm}^2\)
\(\text{0,00045} \text{ m}^2\)
\(\text{72,6} \text{ cm}^2\)

\(\text{340} \text{ mm}^2\)
\(\text{9 000} \text{ mm}^2\)
\(\text{62} \text{ mm}^2\)
\(\text{4 500} \text{ mm}^2\)
\(\text{7 260} \text{ mm}^2\)

Convert each area to square metres.

\(\text{1 753} \text{ cm}^2\)
\(\text{85 000} \text{ mm}^2\)
\(\text{55 010} \text{ cm}^2\)
\(\text{2,04} \text{ km}^2\)
\(\text{360} \text{ cm}^2\)

\(\text{0,1753} \text{ m}^2\)
\(\text{0,085} \text{ m}^2\)
\(\text{5,501} \text{ m}^2\)
\(\text{2 040 000} \text{ m}^2\)
\(\text{0,036} \text{ m}^2\)

Volume is measured in cubic units. The volume of an object can be expressed in cubic millimetres (\(\text{mm}^3\)), cubic centimetres (\(\text{cm}^3\)), cubic metres (\(\text{m}^3\)) and also cubic kilometres (\(\text{km}^3\)).

The diagram below shows how to convert between the different units of volume.

Worked Example 17.12: Converting between units of volume

Convert \(\text{8 259} \text{ mm}^3\) to cubic centimetres.

Divide the volume by \(10^{3}\).

To convert from cubic millimetres to cubic centimetres, we divide the volume by \(10^3 = 1\ 000\):

\[\begin{align} \text{8 259} \text{ mm}^3 &= \text{8 259} \div \text{1 000} \\ &= \text{8,259} \text{ cm}^3 \end{align}\]

Worked Example 17.13: Converting between units of volume

Convert \(\text{3,08} \text{ m}^3\) to cubic centimetres.

Multiply the volume by \(100^{3}\).

To convert from cubic metres to cubic centimetres, we multiply the volume by \(100^3 = 1\ 000\ 000\):

\[\begin{align} \text{3,08} \text{ m}^3 &= \text{3,08} \times \text{1 000 000} \\ &= \text{3 080 000} \text{ cm}^3 \end{align}\]

Capacity can be expressed in millilitres (\(\text{ml}\)), litres (\(\text{l)}\) and kilolitres (\(\text{kl}\)). Capacity can also be measured in cubic centimetres (\(\text{cm}^3\)) and cubic metres (\(\text{m}^3\)).