Targeting Grade C

1
GCSE Mathematics
Targeting Grade C
SSM 5 Volume
2

• Can you
• Calculate the volume of a cuboid?
• Can you calculate the volume of prisms
  (triangular, cylinder, trapezoidal)?
• Solve problems involving volumes of 3D shapes?
• Can you work out a length if you have been given
  the volume?
• Try some questions

Practice 1 Remember the formula for volume of
a cuboid. You will be given the formulae for the
area of a trapezium and the volume of a prism,
but you will need to know the formulae for the
area of a circle and a triangle. Practice 2
Decide which formulae to use when calculating the
volume. Practice 3 Substitute the values given
into the correct formula. Questions
3
Volume of a Cuboid

• The formula for the volume of a cuboid is
• Volume length x breadth x height V l
  x b x h

4
Note that there are 3 dimensions so the units are
cubic m or cm.
Example

• Work out the volume of this cuboid
• V l x b x h
• V 15 x 6 x 10
• V 900cm³

• A cuboid has
• Height 3m
• Length 9m
• Breadth 5m
• What is its volume?
• V l x b x h
• V 3 x 9 x 5
• V 135 m³

5
Practice 1

• Maxine has two boxes in the shape of cuboids.
• Box A measures 123cm by 6cm by 3cm
• Box B measures 9cm by 87cm by 28cm
• Maxine wants to use the box with the greater
  volume
• Give the letter of the box Maxine should use
• You must show all your calculations

Answer
6
Practice 1 answer

• Box A
• V l x b x h
• V 12.3 x 6 x 3
• V 221.4 cm³
• Box B
• V l x b x h
• V 9 x 8.7 x 2.8
• V 219.24cm³
• Box A has the greatest value

7
Area of Circle

• The formula for the area of a circle
• Area pi x radius x radius
• A p x r x r
• A pr²

8
Area of a triangle

• The formula for the area of a triangle is
• Area ½ x base x perpendicular height
• A ½ x b x h.
• A ½bh

9
Example

• Calculate the volume of this trapezoidal
• prism

• Volume of prism is
• Area of cross section x length
• 19.62 x 10
• 196.2cm³

10cm
Area of cross section (trapezium) is ½ (ab)h ½
(4.2 6.7) x 3.6 ½ x 10.9 x 3.6 ½ x
39.24 19.62cm²
Remember 2 dimensions - units² 3 dimensions
units³
10
Example
Area of cross section (triangle) is ½ b x h ½ x 3
x 4 ½ x 12 6cm² Volume of prism is Area of
cross section x length 6 x 11 66cm³
11
Practice 2
(b) BC 4cm, CF 12cm, AB 5cm and angle ABC
is 90. Calculate the volume of the triangular
prism.

• (a)
• The cylinder has a radius of 4cm and a
• height of 15cm. Calculate the volume
• of the cylinder. Give your answer
• correct to 3 significant figures.
• (Take p3.14)

15cm
5cm
4cm
Answer
12
Practice 2 answer

• (a)
• Volume of cylinder area of cross section x h
• V p r² h (Take p 3.14)
• V p x r x r x h
• V 3.14 x 4 x 4 x 15
• V 753.6
• V 754 cm³ (3 SF)
• (b)
• Volume of prism area of cross section x L
• V ½ x b x h x L
• V ½ x 4 x 5 x 12
• V 120 cm³

13
Practice 3A
Answer
(b) Calculate the volume of the silver bar.
14
Practice 3A answer

• Area of cross section (trapezium)
• ½ (a b) x h
• ½ (4 10) x 4
• ½ x 14 x 4
• 28cm²
• Volume of silver bar
• 28 x 15
• 420cm³

15
Practice 3B

• A box in the shape of a cube
• has sides of length 2 cm.
• These cube boxes are placed into
• a larger cuboid box with dimensions
• Height 8cm
• Length 10cm
• Width 6cm
• How many cube boxes fit into the cuboid box
  exactly?

Answer
16
Practice 3B answer

• Volume of small cube
• V l x w x h
• V 2 x 2 x 2
• V 8cm³
• Volume of large cube
• V 6 x 8 x 10
• V 480 cm³
• Number of small cubes in cuboid
• 480 8 60

17
Example

• The base of a cuboid is 10 cm by 10cm.
• The volume of the cuboid is 1420cm³.
• Find the height of the cuboid.
• V l x b x h
• 1420 10 x 10 x h
• 1420 100 x h
• 1420 100 h
• 14.2 h
• So the height of the cuboid is 14.2cm.

h cm
10 cm
10 cm
18
Practice 4A
BC 4cm, CF 12 cm and angle ABC 90. If the
volume of the triangular prism is 84 cm³. What is
the length of the side AB of the prism?
19
Practice 4A answer

• Volume of prism area of cross section x length
• 84 ½ x 4 x AB x 12
• 84 AB x 24
• 84 24 AB
• AB 3.5cm

20
Practice 4B

• A cuboid has a volume of 160 cm³.
• Its length is 8cm and its height is
• 4 cm.
• Work out the breadth of the cuboid.

Answer
21
Practice 4B answer

• Volume of cuboid l x b x h
• 160 8 x 4 x b
• 160 32 x b
• 160 32 b
• b 5 cm

22
Questions
23

• 1. (a) Christopher buys a fish tank.
• The dimensions of the tank are 91 cm by 32 cm by
  35 cm.
• (i) Calculate the volume of the tank in cm³.
• .................................................
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• (ii) How many litres of water will the tank hold
  when full?
• (1000 cm³ 1 litre)
• .................................................
  ..................................................
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  (2)

• Answers

• Volume of a cuboid l x b x h
• V 91 x 32 x 35
• V 101920 cm³

(ii) 101920 1000 101.92 litres
24

• The diagram shows a cuboid.
• The cuboid has a volume of 180 cm3.
• Calculate the height of the cuboid.
• ..................................................
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• ..................................................
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• ..................................................
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• ..................................................
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• Answer

Volume of a cuboid l x b x h V
l x b x h 180 8 x 5 x h 180
40 x h 180 40 h 4.5 h The
height of the cuboid is 4.5cm
25

• The diagram shows a bale of straw.
• The bale is a cylinder with radius 70
• cm and height 50 cm.
• Calculate the volume of the bale.
• State your units.
• ................................................
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• Answer ...........................
  (4)

• Answer

Volume of a cylinder area of cross section x
height Area of cross section pr²
p x 70 x 70
p x 4900 Volume p x 4900
x h p x 4900 x 50 p
x 245000 769689.55
769690 cm³ 769.69 m³
26

• The diagram is a drawing of a triangular prism.
• (a) Calculate the area of triangle ABC.
• .................................................
  ..................................................
  ..................................................
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• (2)
• (b) Calculate the volume of the prism.
• .................................................
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• Answers

Area of a triangle ½ x base x height
½ x 6 x 2
½ x 12 6
cm² (area of cross section)
Volume of prism Area of cross section x length
V 6 x 5
V 30 cm³
27

• The diagram shows a
• ridge tent which is 3.6m
• long.
• Calculate the volume of
• the ridge tent.

• Answer

Area of cross section Area of rectangle 1.9m x
0.8m 1.52m² Area of
triangle ½ x 1.9m x 1.6m(2.4 0.8)
½ x 3.04
1.52m² Area cross section 1.52 1.52
3.04m² Volume of prism Area of cross section
x length
3.04 x3.6
10.944m³
2.4m
0.8m
3.6m
1.9m