YEAR 9 · SURFACE AREA, VOLUME AND MEASUREMENT · 15 MIN

Unit conversion

Convert length, area, volume and capacity using the correct power of the unit scale.

In this lesson

Use squared and cubed conversion factors
Choose a consistent unit before calculating

Before you start

Place value and powers of ten
Area and volume units

01 / LEARN

Understand the idea.

An area contains two dimensions

A square metre is a square with sides $1 m = 100 cm$ . It contains $100$ rows of $100$ square-centimetre tiles, giving $100^{2} = 10000 {cm}^{2}$ . The area factor is the square of the length factor.

Converting to smaller units increases the number of units needed to describe the same area. Multiply square metres by $10000$ to obtain square centimetres; divide by $10000$ to reverse the conversion. The physical area does not change.

1 m^{2} = 10000 {cm}^{2}

Volume contains three dimensions

A cubic metre has three edges of $100 cm$ , so it contains $100^{3} = 1000000 {cm}^{3}$ . For volume conversions, cube the length factor. Using the area factor would count layers in only two dimensions.

Capacity provides a useful check: $1 m^{3} = 1000 L$ and $1 L = 1000 {cm}^{3}$ . Before calculating area or volume with mixed lengths, convert all dimensions to one length unit, then apply the formula.

1 m^{3} = 1000000 {cm}^{3} = 1000 L

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert a floor area

Convert 2.4 m² into square centimetres.

Worked solution

1
Establish the area conversion.
$1 m^{2} = {(100 cm)}^{2} = 10000 {cm}^{2}$
Both dimensions change by the length factor $100$ .
2
Apply it to the given area.
$2.4 m^{2} = 2.4 \times 10000 = 24000 {cm}^{2}$
There are $2.4$ lots of one square metre.
3
Check the conversion direction.
$24000 \div 10000 = 2.4$
Smaller area units give a larger numerical count, and the reverse calculation recovers the original area.

Answer

24,000 cm²

EXAMPLE 02

Connect volume and capacity

Convert 0.035 m³ into litres and cubic centimetres.

Worked solution

1
Convert cubic metres to litres.
$0.035 m^{3} = 0.035 \times 1000 = 35 L$
Each cubic metre holds one thousand litres.
2
Use the cubic length factor.
$0.035 m^{3} = 0.035 \times 100^{3} = 35000 {cm}^{3}$
Three length dimensions each change from metres to centimetres.
3
Cross-check using capacity.
$35 L = 35 \times 1000 = 35000 {cm}^{3}$
The capacity route and cubic-unit route describe the same volume.

Answer

35 L and 35,000 cm³

03 / YOUR TURN

Try it yourself.

Check your understanding

Is 1 m² equal to 100 cm² or 10,000 cm²?

Show answer & reasoning

10,000 cm².

A square metre contains $100$ one-centimetre rows with $100$ tiles in each row: $100 \times 100 = 10000 {cm}^{2}$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Convert 3.2 m to centimetres.
1 mark
Convert 450 cm² to square metres.
2 marks
Convert 0.006 m³ to cubic centimetres.
2 marks
Convert 7500 mL to litres.
1 mark
Convert 0.82 m² to square centimetres.
2 marks
A prism has internal dimensions 12 cm, 8 cm and 0.5 m. Find its capacity in litres.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 3.2 m to centimetres.
1 mark
$3.2 \times 100 = 320$ cm.
320 cm
Convert 450 cm² to square metres.
2 marks
$450 \div 10000 = 0.045$ m².
0.045 m²
Convert 0.006 m³ to cubic centimetres.
2 marks
$0.006 \times 1000000 = 6000$ cm³.
6000 cm³
Convert 7500 mL to litres.
1 mark
$7500 \div 1000 = 7.5$ L.
7.5 L
Convert 0.82 m² to square centimetres.
2 marks
$0.82 \times 10000 = 8200$ cm².
8200 cm²
A prism has internal dimensions 12 cm, 8 cm and 0.5 m. Find its capacity in litres.
3 marks
$0.5$ m $= 50$ cm. Volume $= 12 \times 8 \times 50 = 4800$ cm³.
$4800 \div 1000 = 4.8$ L.
4.8 L

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 / South Australian Curriculum

Year 9 surface area and volume of right prisms and cylinders, capacity, absolute/relative/percentage measurement error, precision and practical measurement problems.

Official curriculum source ↗

In this lesson

Understand the idea.

An area contains two dimensions

Volume contains three dimensions

See the method in action.

Convert a floor area

Establish the area conversion.

Apply it to the given area.

Check the conversion direction.

Connect volume and capacity

Convert cubic metres to litres.

Use the cubic length factor.

Cross-check using capacity.

Try it yourself.

Check your understanding

Keep practising