KS3

Converting metric units for area and volume

Part ofMathsMeasurement

Key points

A series of two images. Each image shows the same cube. In the first cube the length, width and height are labelled as one metre. Written below: one metre multiplied by one metre multiplied by one metre equals one metre cubed. In the second cube the length, width and height are labelled as one hundred centimetres. Written below: one hundred centimetres multiplied by one hundred centimetres multiplied by one hundred centimetres equals one million centimetres cubed.

and are usually measured in metric units. An area can be measured in centimetres squared (cm²) or metres squared (m²). Volume is often measured in centimetres cubed (cm³) or metres cubed (m³).
When comparing or combining an area or volume it is important to measure the objects using the same units. Without converting the areas into the same unit, it might be difficult to tell, for example, whether 400cm² is bigger (or smaller) than 4m².
A common could be when someone thinks that the conversion between two different lengths would be the same conversion between two different areas. For example, 1 m is the same as 100 cm but 1 m² is not the same as 100 cm².

A series of two images. Each image shows the same cube. In the first cube the length, width and height are labelled as one metre. Written below: one metre multiplied by one metre multiplied by one metre equals one metre cubed. In the second cube the length, width and height are labelled as one hundred centimetres. Written below: one hundred centimetres multiplied by one hundred centimetres multiplied by one hundred centimetres equals one million centimetres cubed.

Converting units for area

Objects can be measured in different units, depending on their size. It is important to know the conversions between metric units.
The method for converting between units for works in a similar way to converting between units of length. However, it is important to remember that an area has two .
When you are converting one type of unit to another you need to know how many smaller units are needed to make one larger unit.

Examples

Skip image gallery

Image caption,
Work out how many centimetres squared (cm²) would be needed to cover an area of 1 metre squared (1 m²)
Image caption,
A common misconception would be that 100 cm² are needed because 1 metre is 100 centimetres. This is incorrect.
Image caption,
When converting between units for an area calculation, remember that a square has two dimensions, the length and the width. Draw two identical squares next to one another. Label one in metres (1 m by 1 m). 1 metre is equivalent to 100 centimetres. Label the other square in centimetres (100 cm by 100 cm).
Image caption,
The area of the square labelled in metres is 1 m x 1 m = 1 m². The area of the square labelled in centimetres is 100 cm x 100 cm = 10,000 cm².
Image caption,
10,000 square centimetres would be needed to create the same area as 1 metre square.
Image caption,
When converting between units for an area calculation convert both dimensions (the length and width) to the required unit before finding the area. Use these to calculate the area conversion factor. When converting from a larger unit to a smaller unit (eg m² to cm²) you multiply. When converting from a smaller unit to a larger unit (eg mm² to cm²) you divide.
Image caption,
Convert 60,000 cm² into m². 1 m = 100 cm. 1 m² = 100 cm x 100 cm = 10, 000 cm². Conversion factor is 10,000
Image caption,
The smaller unit (cm²) is converted to a larger unit (m²). To do this, divide 60,000 cm² = 60,000 ÷ 10,000 = 6 m².
Image caption,
Convert 20 cm² into mm². 1 cm = 10 mm. 1 cm² = 10 mm x 10 mm = 100 mm². Conversion factor is 100
Image caption,
The larger unit (m²) is converted to a smaller unit (cm²). To do this, multiply 20 cm² = 20 × 100 = 2,000 mm².

Question

What is the area of a 3 m by 2 m rectangle in square centimetres?

An image of a rectangle. The length of the rectangle has been labelled as three metres. The width of the rectangle has been labelled as two metres. The rectangle is coloured yellow.

Converting units for volume

Objects can be measured in different units, depending on their size. It is important to know the conversions between metric units.
The method for converting between units for works in a similar way to converting between units of length, however it is important to remember that a volume has three .
When you are converting one type of unit to another you need to know how many smaller units are needed to make 1 larger unit.

Examples

Skip image gallery

Image caption,
Work out how many centimetres cubes would be needed to equal a volume of 1 metre cubed.
Image caption,
A common misconception would be that there would be 100 because 1 metre is 100 centimetres. This is incorrect, however.
Image caption,
When converting between units for a volume calculation it is important to remember that a cube has three dimensions: length, width and height. Draw two identical cubes next to one another. Label one in metres (1 m by 1 m by 1 m). 1 metre is equivalent to 100 centimetres. Label the other cube in centimetres (100 cm by 100 cm by 100 cm).
Image caption,
The volume of the cube labelled in metres is 1 m x 1 m x 1 m = 1 m³. The volume of the cube labelled in centimetres is 100 cm x 100 cm x 100 cm = 1,000,000 cm³.
Image caption,
1,000,000 cubic centimetres would be needed to create the same volume as 1 metre cubed.
Image caption,
When converting between units for a volume calculation convert all three dimensions (the length, width and height) to the required unit before finding the volume. Use these to calculate the volume conversion factor. When converting from a larger unit to a smaller unit (eg m³ to cm³) you multiply. When converting from a smaller unit to a larger unit (eg mm³ to cm³) you divide.
Image caption,
Convert 50,000 mm³ into cm³. 1 cm = 10 mm. 1 cm³ = 10 mm x 10 mm x 10 mm = 1000 mm³. Conversion factor is 1000
Image caption,
The smaller unit (cm³) is converted to a larger unit (m³). To do this, divide 50,000 mm³ = 50,000 ÷ 1000 = 50 cm³.
Image caption,
Convert 4 m³ into cm³. 1 m = 100 cm. 1 m³ = 100 cm x 100 cm x 100 cm = 1,000,000 cm³. Conversion factor is 1,000,000
Image caption,
The larger unit (m³) is converted to a smaller unit (m³). To do this, multiply 4m³ = 4 × 1,000,000 = 4,000,000 cm³.

Question

What would the dimensions of the cuboid be in centimetres?

An image of a cuboid. The length of the cuboid has been labelled as four thousand millimetres. The width of the cuboid has been labelled as two metres. The height of the cuboid has been labelled as one thousand eight hundred millimetres. The cuboid is coloured blue.

Practise working out how to convert metric units for area and volume

Practise working out how to convert metric units for area and volume with this quiz. You may need a pen and paper to help you with your answers.

Quiz

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