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17.5 The volumes and surface areas of cuboids

17.5 The volumes and surface areas of cuboids

Do you remember the formulae for the volume and surface area of a cuboid?
For a cuboid with length l, width w and height h: h
volume = length × width × height w
l
or V = lwh
surface area = 2 × length × width + 2 × length × height + 2 × width × height
or SA = 2lw + 2lh + 2wh
Remember: when you use these formulae, the measurements for length, width and height must
be in the same units.

Worked example 17.5

a Work out the volume and surface area of this cuboid.
8 mm
3
b A cuboid has a volume of 60 cm .
4 cm
The length of the cuboid is 5 cm.
6 cm
The height of the cuboid is 4 cm.
Work out the width of the cuboid.
a 8 mm = 0.8 cm The height of the cuboid is given in mm. Change this to
cm so that all the measurements are in the same units.
V = l × w × h Write down the formula you are going to use for the
V = 6 × 4 × 0.8 volume.
3
= 19.2 cm Substitute the numbers into the formula.
3
Work out the answer and remember the units (cm ).
Write down the formula you are going to use for the
SA = 2lw + 2lh + 2wh surface area.
= 2 × 6 × 4 + 2 × 6 × 0.8 + 2 × 4 × 0.8 Substitute the numbers into the formula.
= 48 + 9.6 + 6.4 Work out all the multiplications.
2
2
= 64 cm Work out the answer and remember the units (cm ).
b V = l × w × h Write down the formula you are going to use for the volume.
60 = 5 × w × 4 Substitute the numbers that you know into the formula to
make an equation, with w as the unknown.
60 = 20 × w Simplify the right-hand side of the equation; 5 × 4 = 20.
60
w = = 3 cm Divide 60 by 20 to work out the value of w. Remember to
20
include the units (cm) in your answer.

Exercise 17.5

1 Work out the volume of each cuboid.
a b c 1.5 m
6 mm
4 m
9 cm
10 m
3 cm 12 mm
7 cm
8 mm
2 Work out the surface areas of the cuboids in question 1.

17 Area, perimeter and volume 173