Page 177 - Cambridge Checkpoint Mathematics Coursebook 7_Slide

18.4 Calculating the volume of cuboids

18.4 Calculating the volume of cuboids

Look at this cube. It has a length, a width and a height of 1 cm. 1 cm
It is called a centimetre cube. You say that it has a volume of one
cubic centimetre (1 cm ). 1 cm 1 cm
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NOT TO SCALE
2 cm
is cuboid is 4 cm long, 3 cm wide and 2 cm high.
If you divide the cuboid into centimetre cubes, it
3 cm
looks like this. 2 cm
4 cm
3 cm
4 cm
2 cm

3 cm
4 cm
2 cm
You can see that there are 12 cubes in each layer and that there are two layers. is means that the total
number of centimetre cubes in this cuboid is 24. 4 cm 3 cm
You say that the volume of the cuboid is 24 cm . h
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You can work out the volume of a cuboid, using the formula:
volume = length × width × height w

or V = l × w × h l

If the sides of a cuboid are measured in millimetres, the volume will be in cubic millimetres (mm ).
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Ifthe sides of a cuboid are measured in metres, the volume will be in cubic metres (m ).
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Worked example 18.4

a Work out the volume of this cuboid. 3 cm
b A concrete cuboid has a length of 5.1 m, a width of 3.2 m
and a height of 1.8 m. 5 cm
i Work out the volume of the cuboid.
Ii Use estimation to check your answer. 8 cm

a V = 8 × 5 × 3 Use the formula: volume = length × width × height.
= 120 cm All the lengths are in cm so the answer is in cm .
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b i V = 5.1 × 3.2 × 1.8 Use the formula: volume = length × width × height.
= 29.376 m All the lengths are in m so the answer is in m .
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ii V = 5 × 3 × 2 To estimate, round all the lengths to the nearest whole number.
= 30 m 30 is close to 29.376 so the answer to part bi is probably correct.
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✦ Exercise 18.4

1 Work out the volume of each of these cuboids.
a b c
2 cm 1 cm
3 cm
4 cm 6 cm
7 cm 6 cm 9 cm

5 cm
18 Area, perimeter and volume 175