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Conversion of units Area of rectangles DecimalsVolume

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Converting metric units Surface areaThis topic is relevant for:

Here we will learn about converting units of area and volume.

There are also worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Converting units of area and volume** is converting between different units from the metric system involving area and volume.

To do this we need to be able to convert between different units of length, and then adapt them for area and volume.

We know that 1 \ m =100 \ cm and 1 \ cm =10 \ mm , so we can convert between these lengths:

**Step-by-step guide:** Converting metric units

We can then apply these to units of measurement for area and volume.

Let’s apply this to area:

We know that 1 \ cm = 10 \ mm

So, 1 \ cm^2 = 10 \times 10 =10^2 =100 \ mm^2

Similarly we know that 1 \ m = 100 \ cm

So, 1 \ m^2 = 100 \times 100 =100^2 =10 \ 000 \ cm^2

Let’s apply this now to volume:

We know that 1 \ cm =10 \ mm

So, 1 \ cm^3 =10 \times 10 \times 10 =10^3 =1000 \ mm^3

Similarly we know that 1 \ m = 100 \ cm

So, 1 \ m^3 =100 \times 100 \times 100 =100^3 =1 \ 000 \ 000 \ cm^3

E.g.

Convert 7 \ m^2 to cm^2

7\times 100^2 =70\ 000So, 7 \ m^2 = 70 \ 000 \ cm^2

In order to convert units of area and volume:

**Find the unit conversion.****Square or cube the unit conversion.****Multiply or divide.**

Get your free converting units of area and volume worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free converting units of area and volume worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE**Converting units of area and volume** is part of our series of lessons to support revision on **units of measurement**. You may find it helpful to start with the main units of measurement lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Convert 3 \ m^2 to cm^2

**Find the unit conversion.**

The units involve metres and centimetres

1 \ m=100 \ cm2**Square or cube the unit conversion.**

The question involves square units, so we need to square the unit conversion.

100^2 = 10\ 0003**Multiply or divide.**

As we are going from larger units to smaller units we multiply.

3 \times 100^2 = 3 \times 10 \ 000=30 \ 000So, \ 3 \ m^2 \ is \ 30 \ 000 \ cm^2

Convert 45 \ 000 \ cm^2 to m^2

**Find the unit conversion.**

The units involve metres and centimetres

1 \ m= 100 \ cm

**Square or cube the unit conversion.**

The question involves square units, so we need to square the unit conversion.

100^2 =10 \ 000

**Multiply or divide.**

As we are going from smaller units to larger units we divide.

45 \ 000 \div 100^2 =45 \ 000 \div 10 \ 000 =4.5

So, \ 45 \ 000 \ cm^2 \ is \ 4.5 \ m^2

Convert 6.1 \ cm^2 to mm^2

**Find the unit conversion.**

The units involve centimetres and millimetres

1 \ cm= 10 \ mm

**Square or cube the unit conversion.**

The question involves square units, so we need to square the unit conversion.

10^2 =100

**Multiply or divide.**

As we are going from larger units to smaller units we multiply.

6.1 \times 10^2 = 6.1 \times 100 =610

So, \ 6.1 \ cm^2 \ is \ 610 \ mm^2

Convert 7800 \ mm^2 to cm^2

**Find the unit conversion.**

The units involve centimetres and millimetres

1 \ cm= 10 \ mm

**Square or cube the unit conversion.**

The question involves square units, so we need to square the unit conversion.

10^2 =100

**Multiply or divide.**

As we are going from smaller units to larger units we divide.

7800 \div 10^2 =7800 \div 100 = 78

So, \ 7800 \ mm^2 \ is \ 78 \ cm^2

Convert 5 \ cm^3 to mm^3

**Find the unit conversion.**

The units involve centimetres and millimetres

1 \ cm = 10 \ mm

**Square or cube the unit conversion.**

The question involves cubic units, so we need to cube the unit conversion.

10^3 =1000

**Multiply or divide.**

As we are going from larger units to smaller units we multiply.

5 \times 10^3 =5 \times 1000=5000

So, \ 5 \ cm^3 \ is \ 5000 \ mm^3

Convert 68 \ 000 \ mm^3 to cm^3

**Find the unit conversion.**

The units involve centimetres and millimetres

1 \ cm = 10 \ mm

**Square or cube the unit conversion.**

The question involves cubic units, so we need to cube the unit conversion.

10^3 = 1000

**Multiply or divide.**

As we are going from smaller units to larger units we divide.

68 \ 000 \div 10^3 =68 000 \div 1000=68

So, \ 68 \ 000 \ mm^3 \ is \ 68 \ cm^3

**Remember to square or cube the unit conversion**

You need to remember to square the unit conversion for units of area.

You need to remember to cube the unit conversion for units of volume.

E.g. convert 3 \ m^2 to cm^2

This would be **incorrect** \; \color{red} ✘

3 \times 100=300

This would be **correct** \; \color{green} ✔

3 \times 100^2 =3 \times 10 \ 000 = 30 \ 000

3 \ m^2 =30 \ 000 \ cm^2

1. Convert: \ 5.6 \ m^2 to cm^2

5\ 600 \ cm^2

56\ 000 \ cm^2

560 \ cm^2

560\ 000 \ cm^2

We need to multiply by 100^2 as we are converting m^2 to cm^2

5.6\times 100^2 = 5.6 \times 10\ 000 = 56\ 000

2. Convert: \ 840 \ 000 \ cm^2 to m^2

84\ 000 \ m^2

840 \ m^2

8\ 400 \ m^2

84 \ m^2

We need to divide by 100^2 as we are converting cm^2 to m^2

840\ 000\div 100^2 = 840\ 000\div 10\ 000 = 84

3. Convert: \ 94 \ cm^2 to mm^2

9.4 \ mm^2

940 \ mm^2

9\ 400 \ mm^2

0.94 \ mm^2

We need to multiply by 10^2 as we are converting cm^2 to mm^2

94\times 10^2 = 94\times 100 = 9 \ 400

4. Convert: \ 570 \ mm^2 to cm^2

5.7 \ cm^2

57 \ cm^2

0.57 \ cm^2

5\ 700 cm^2

We need to divide by 10^2 as we are converting mm^2 to cm^2

570\div 10^2 = 570\div 100 = 5.7

5. Convert: \ 6.3 \ cm^3 to mm^3

63 \ mm^3

630 \ mm^3

0.63 \ mm^3

6\ 300 \ mm^3

We need to multiply by 10^3 as we are converting cm^3 to mm^3

6.3\times 10^3 = 6.3\times 1000 = 6\ 300

6. Convert: \ 9 \ 100 \ mm^3 to cm^3

91\ 000 \ cm^3

91 \ cm^3

9.1 \ cm^3

910 \ cm^3

We need to divide by 10^3 as we are converting mm^3 to cm^3

9 \ 100\div 10^3 = 9 \ 100\div 1000 = 9.1

1. Write 35 \ cm^3 in mm^3

**(2 marks)**

Show answer

35\times 10^3

**(1)**

35 \ 000

**(1)**

2. Write 48 \ m^2 in cm^2

**(2 marks)**

Show answer

48\times 100^2

**(1)**

480 \ 000

**(1)**

3. In the garden there is an area that needs covering with bark chippings.

The area is 210 \ 000 \ cm^2.

A bag of bark chippings covers 4 \ m^2.

How many bags of bark chippings are needed to be bought to cover the area?

**(3 marks)**

Show answer

210\ 000\div 100^2=21

**(1)**

21\div 4=5.25

**(1)**

6 bags are needed to be bought.

(Rounding up as we can only buy full bags.)

**(1)**

You have now learned how to:

- Convert metric units of area
- Convert metric units of volume

There are non-metric units of area and non-metric units of volume.

These are called imperial units.

**Imperial units of area**

There are non-metric units that can be used for area.

E.g.

There are 12 inches in 1 foot.

If we wanted to convert between square inches and square feet we would use the multiplier 12^2 .

So 5 square feet would be 5 \times 12^2 square inches which is 720 square inches.

We can do a similar thing for square feet and square yards.

E.g.

There are 3 feet in 1 yard, so we would use 3^2 to convert between square feet and square yards.

This can be extended to the square mile.

E.g.

There are 1760 yards in 1 mile, so we would use 1760^2 to convert between square feet and square miles.

**Imperial units of volume**

There are non-metric units that can be used for volume.

E.g.

There are 12 inches in 1 foot.

If we wanted to convert between cubic inches and cubic feet we would use the multiplier 12^3 .

So 4 cubic feet would be 4 \times 12^3 cubic inches which is 6912 cubic inches.

We can do similar for cubic feet and cubic yards.

E.g.

There are 3 feet in 1 yard, so we would use 3^3 to convert

between cubic feet and cubic yards.

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