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Converting between different units

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.

  1. \(\text{2,06} \text{ m}^2\)
  2. \(\text{7 423} \text{ mm}^2\)
  3. \(\text{0,015} \text{ m}^2\)
  4. \(\text{842,5} \text{ mm}^2\)
  5. \(\text{0,416} \text{ m}^2\)
  1. \(\text{20 600} \text{ cm}^2\)
  2. \(\text{74,23} \text{ cm}^2\)
  3. \(\text{150} \text{ cm}^2\)
  4. \(\text{8,425} \text{ cm}^2\)
  5. \(\text{4 160} \text{ cm}^2\)

Convert each area to square millimetres.

  1. \(\text{3,4} \text{ cm}^2\)
  2. \(\text{0,009} \text{ m}^2\)
  3. \(\text{0,62} \text{ cm}^2\)
  4. \(\text{0,00045} \text{ m}^2\)
  5. \(\text{72,6} \text{ cm}^2\)
  1. \(\text{340} \text{ mm}^2\)
  2. \(\text{9 000} \text{ mm}^2\)
  3. \(\text{62} \text{ mm}^2\)
  4. \(\text{4 500} \text{ mm}^2\)
  5. \(\text{7 260} \text{ mm}^2\)

Convert each area to square metres.

  1. \(\text{1 753} \text{ cm}^2\)
  2. \(\text{85 000} \text{ mm}^2\)
  3. \(\text{55 010} \text{ cm}^2\)
  4. \(\text{2,04} \text{ km}^2\)
  5. \(\text{360} \text{ cm}^2\)
  1. \(\text{0,1753} \text{ m}^2\)
  2. \(\text{0,085} \text{ m}^2\)
  3. \(\text{5,501} \text{ m}^2\)
  4. \(\text{2 040 000} \text{ m}^2\)
  5. \(\text{0,036} \text{ m}^2\)

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 (\(\text{m}^3\)).

  • \(1 \text{ cm}^3 = 1 \text{ ml}\)
  • \(1\ 000 \text{ cm}^3 = 1 \text{ litre}\)

Worked Example 17.14: Converting between units of volume and capacity

Convert \(560 \text{ cm}^3\) to litres.

Divide the volume by \(1\ 000\).

To convert from cubic centimetres to litres, we divide the volume by \(1\ 000\):

\[1 \text{ cm}^3 = 1 \text{ ml}\]

So \(560 \text{ cm}^3 = 560 \text{ ml}\).

And we know that \(\text{1 000} \text{ ml} = 1 \text{ litre}\).

Therefore,

\[\begin{align} \text{560} \text{ cm}^3 &= \text{560} \div \text{1 000} \\ &= \text{0,56} \text{ litres} \end{align}\]
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