Converting units: area and volume

In a nutshell

Area and volume unit conversions are almost identical to regular unit conversions except for one thing: they involve multiply or dividing by the conversion factor more than once.

Area unit conversions

When converting between units of area, the steps are very similar to converting with regular lengths. However, since area is measured in units squared, multiplying and dividing by the conversion factor has to happen twice.

PROCEDURE

1.	Identify the conversion factor.
2.	Decide whether to divide or multiply.
3.	Divide or multiply by the conversion factor *twice.*

Tip: Remember the units in your answer should be squared (followed by a $^2$ ).

Example 1

Take a look at the $1m \times 1m$ cube. What is its area in metres squared?

Work out the area in metres squared.

1\times1=1m^2

Identify the conversion factor.

1m=100cm

Conversion factor =

100

Multiply by the conversion factor twice to go from metres squared (big) to centimetres squared (small).

1m^2\times100\times100=\underline{10,000cm^2}

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: area and volume

Example 2

What is the area of the rectangle? Give your answer in metres squared.

Work out the area in centimetres squared.

$3\times5=15cm^2$

Identify the conversion factor.

$1m=100cm$

Conversion factor $=100$

Divide by the conversion factor twice to go from centimetres squared (small) to metres squared (big).

5cm^2\div100\div100=\underline{0.0015m^2}

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: area and volume

Volume unit conversions

Volume unit conversions are treated in the same way as area conversions except that instead of multiplying/dividing twice, it happens three times.

PROCEDURE

1.	Identify the conversion factor.
2.	Decide whether to divide or multiply.
3.	Divide or multiply by the conversion factor three times.

Tip: Remember the units in your answer should be cubed (followed by a $^3$ ).

Example 3

The cuboid shown has a volume of $2.5m^3$ . What is its volume in centimetres cubed?

Work out the conversion factor.

$1m=100cm$

Conversion factor $=100$

Multiply by the conversion factor three times to go from metres cubed (big) to centimetres cubed (small).

$2.5m^3\times100\times100\times100=\underline{2,500,000cm^3}$

Maths; Ratio proportion and rates of change; KS4 Year 10; Converting units: area and volume