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

Breadth – b = 6m

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

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