Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 1 • Question 2

Circle the volume that is the same as 0.3 m³. [A] 30 cm³ [B] 3000 cm³ [C] 30000 cm³ [D] or is it 300000 cm³?

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Video Transcript

Circle the volume that is the same as 0.3 metres cubed. Is it 30 centimetres cubed, 3000 centimetres cubed, 30000 centimetres cubed, or is it 300000 centimetres cubed?

We know that one metre is equal to 100 centimetres. Be careful though. This does not mean that 0.3 metres cubed can be changed to centimetres cubed by multiplying by 100. In fact, we can work out what’s happening by drawing a little sketch of a cube.

This cube is one metre tall, one metre wide, and one metre in depth. Its volume can be calculated by multiplying these three measurements together. That’s one times one times one, which is equal to one. So the volume of this cube is one metre cubed.

But we know that one metre is equal to 100 centimetres. So we can say that this very same cube is 100 centimetres by 100 centimetres by 100 centimetres. This time, the volume is measured in centimetres cubed. It’s 100 times 100 times 100. 100 times 100 times 100 is 1000000. So the volume of the cube is 1000000 centimetres cubed.

Remember, we said these cubes are identical. So we now know that one metre cubed is equal to 1000000 centimetres cubed. We can therefore change from 0.3 metres cubed into centimetres cubed by multiplying by 1000000. When we multiply by 1000000, we move the digits to the left six times. 1000000 multiplied by 0.3 is 300000. So 0.3 metres cubed is equal to 300000 centimetres cubed, and we’re done.

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