Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Converting units of area and volume

Why cm^2 and cm^3 conversions are not the same as lengths.

11 original questions, 27 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Change 3.5 m2 to cm2.

1 mark
Show answer
35000 cm2
2

Change 25 000 cm2 to m2.

1 mark
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2.5 m2
3

Change 6 cm3 to mm3.

1 mark
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6000 mm3
4

Change 450 mm2 to cm2.

1 mark
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4.5 cm2
5

Use 1 litre = 1000 cm3.

  1. Change 2.4 litres to cm3.
  2. Change 7500 cm3 to litres.
2 marks
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a) 2400 cm3 b) 7.5 litres
6

Change 0.35 m3 to cm3.

2 marks
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350 000 cm3
7

1 km2 = 1 000 000 m2 and 1 hectare = 10 000 m2.

  1. A nature reserve has an area of 0.6 km2. Write this area in m2.
  2. Write the area of the reserve in hectares.
  3. A farmer owns 3.5 hectares of land. Write this in m2.
3 marks
Show answer
a) 600 000 m2 b) 60 hectares c) 35 000 m2
8

A rectangular water tank measures 2 m by 1.5 m by 80 cm. 1 m3 = 1000 litres.
Work out how many litres of water the tank holds when it is full.

3 marks
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2400 litres
9

A rectangular floor measures 3.2 m by 2.4 m. It is covered with square tiles of side 20 cm.
Work out how many tiles are needed. Assume there is no gap between tiles and none are cut.

4 marks
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192
10

Water flows out of a pipe at a rate of 0.9 m3 per minute.

1 m3 = 1000 litres

Work out the rate of flow in litres per second.

4 marks
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15 litres per second
11

Room A has a floor area of 84 m2 and is shared by 24 people.

Room B has a floor area of 540 000 cm2 and is shared by 15 people.

  1. Which room gives more floor area per person? You must show your working.
  2. Cal says "540 000 cm2 = 5400 m2 because 100 cm = 1 m". Explain the mistake Cal has made.
5 marks
Show answer
a) Room B; 3.6 m2 per person compared with 3.5 m2 per person b) 1 m2 = 100 x 100 = 10 000 cm2, so he should divide by 10 000, not 100

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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