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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
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
• 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
10 cm
6 cm
15 cm
Note that there
are 3
dimensions so
the units are
cubic m or cm.
Example
Practice 1
• Maxine has two boxes in the
shape of cuboids.
• Box A measures 12·3cm by
6cm by 3cm
• Box B measures 9cm by 8·7cm
by 2·8cm
• 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
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
Area of Circle
The formula for the area of a circle
Area = pi x radius x radius
A = π x r x r
A = πr²
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
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
Remember
2 dimensions - units²
3 dimensions – units³
10cm
Area of cross section (trapezium) is
½ (a+b)h
½ (4.2 + 6.7) x 3.6
½ x 10.9 x 3.6
½ x 39.24
19.62cm²
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
Practice 2 (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 π=3.14)
15cm
4cm
(b)
BC = 4cm, CF = 12cm, AB =
5cm and angle ABC is 90°.
Calculate the volume of the
triangular prism.
5cm
Answer
Practice 2 answer
(a)
Volume of cylinder = area of cross section x h
V = π r² h (Take π = 3.14)
V = π 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
Practice 3A
(b) Calculate the volume of the silver bar.
Answer
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
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?
2cm 6cm
10cm
8cm
Answer
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
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
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?
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
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
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
Questions
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.
............................................................................................................................................................................................................................................
(ii) How many litres of water will the tank hold when full?
(1000 cm³ = 1 litre)
...................................................................................................................................................................................................................................................... (2)
Answers
3 5 c m
3 2 c m9 1 c m
(i) Volume of a cuboid = l x b x h
V = 91 x 32 x 35
V = 101920 cm³
(ii) 101920 ÷ 1000 = 101.92 litres
The diagram shows a cuboid.
The cuboid has a volume of 180 cm3.
Calculate the height of the cuboid.
..............................................................................................................................................
................................................................................................................................................
................................................................................................................................................
................................................................................................................................................
Answer .................................................... cm
Answer
8 c m 5 c m
H e ig h t
N o t to s c a le
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
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.
....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Answer ........................... (4)
Answer
5 0 c m N o t to s c a le
7 0 c m
Volume of a cylinder
= area of cross section x height
Area of cross section = πr²
= π x 70 x 70
= π x 4900
Volume = π x 4900 x h
= π x 4900 x 50
= π x 245000
= 769689.55
= 769690 cm³
= 769.69 m³
The diagram is a drawing of a triangular prism.
(a) Calculate the area of triangle ABC.
.....................................................................................................................................................................................................................................................................................................................................................................................................
(2)
(b) Calculate the volume of the prism.
.....................................................................................................................................................................................................................................................................................................................................................................................................
(2)
Answers
6 c m
5 c m2 c m
A
B C
D
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
The diagram shows a
ridge tent which is 3.6m
long.
Calculate the volume of
the ridge tent.
Answer
3.6m
2.4m
1.9m
0.8m
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
