# VOLUME OF SOLIDS

Volume of Solids
As treated in the previous class, common solids include cubes, cuboids, cones, etc.
Volume of Cuboid
The volume of a cuboid is given by
V = length x breadth x height
V = l x b x h
The unit is m3
Example 1
The length of a cuboid is 5m, its breadth is 6m and height 4m. Calculate its volume.
Solution
Length – l = 5m
Height – h = 4m

V = l x b x h
= 5m x 6m x 4m
= 120m3

Volume of Cubes
All the sides of a cube are equal. Hence,
Volume = l x l x l
V = l3

Example 1
The length of a cube is 5m. Find its volume
Solution
l = 5m
V = l3
V= 53
V = 125m3
Example 2
A concrete beam is 10m long. Its end face is a rectangle of 30cm by 40cm. Calculate its volume. Find the mass of the beam if 1m3 of concrete is 3.5 tonnes.
Solution
Convert
30cm = 0.3m
40cm = 0.4m
Length = 10m
Volume = 10m x 0.3m x 0.4m
= 1.2m3
1m3 = 3.5tonnes
Therefore 1.2m3 = 1.2 x 3.5
= 4.2tonnes

Volume of a right angled triangular prism
Since a right angled triangular prism has a base that is right angled, then its volume is
V = Area of a right angle x height
V = ½bh x h
Example
A prism has a right angled base of base 2m and height 3m. If the height of the prism is 5m. Find the volume of the prism.
Solution
Base of triangle = 2m
Height of triangle = 3m
Height of prism = 5m
V = ½bh x h
V = ½ (2 x 3) x 5
= 3 x 5
V = 15m3
Assignment
Page 132, exercise 16a, numbers 3, 4, 5, 7, 11