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Converting units: area and volume

Converting units: area and volume

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Explainer Video

Tutor: Alice

Summary

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 2^22).


Example 1

Take a look at the 1m×1m1m \times 1m 1m×1m cube. What is its area in metres squared?

Work out the area in metres squared.
1×1=1m21\times1=1m^21×1=1m2

Identify the conversion factor.
1m=100cm1m=100cm1m=100cm
Conversion factor = 100100100​​

Multiply by the conversion factor twice to go from metres squared (big) to centimetres squared (small).
1m2×100×100=10,000cm2‾1m^2\times100\times100=\underline{10,000cm^2}1m2×100×100=10,000cm2​​​
​
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.

3×5=15cm23\times5=15cm^23×5=15cm2


Identify the conversion factor.

1m=100cm1m=100cm1m=100cm

Conversion factor =100=100=100​​

​

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

5cm2÷100÷100=0.0015m2‾5cm^2\div100\div100=\underline{0.0015m^2}5cm2÷100÷100=0.0015m2​​​

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 3^33​).


Example 3

The cuboid shown has a volume of 2.5m32.5m^32.5m3. What is its volume in centimetres cubed?​

Work out the conversion factor.

1m=100cm1m=100cm1m=100cm

Conversion factor =100=100=100​


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

2.5m3×100×100×100=2,500,000cm3‾2.5m^3\times100\times100\times100=\underline{2,500,000cm^3}2.5m3×100×100×100=2,500,000cm3​

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


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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Volume: Comparing, adding and subtracting

Unit 1

Volume: Comparing, adding and subtracting

Formulae for the area and volume of shapes

Unit 2

Formulae for the area and volume of shapes

Jump Ahead

Score 80% to jump directly to the final unit.

This is the current lesson and goal (target) of the path

Converting units: area and volume

Unit 3

Converting units: area and volume

Final Test

Test reviewing all units to claim a reward planet.

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FAQs - Frequently Asked Questions

How do I convert between units of volume?

To convert between units of volume: 1. Identify the conversion factor. 2. Decide whether to divide or multiply. 3. Divide or multiply by the conversion factor three times.

How do I convert between units of area?

To convert between units of area: 1. Identify the conversion factor. 2. Decide whether to divide or multiply. 3. Divide or multiply by the conversion factor twice.

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