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Volume of a Cuboid

The volume of a cuboid can be measured by counting the number of unit cubes it contains.

3 4
6
4 4 4
The volume of the given cuboid is 72 cubic The volume of the given cube is 64 cubic units
units (24 cubes in each of the 3 layers). (16 cubes in each of the 4 layers).
Or 24 × 3 = 72 cubic units. Or 16 × 4 = 64 cubic units.

Quick Check
Find the volume of the following solids formed by the unit cubic blocks.
1. 2. 3.
2 1
4
3 6
6 6
9 1
Also, other than counting the number of unit cubes, we can find the volume of a solid by using
the formulae on the dimensions of the solids.
Let us consider the cuboid made with 72 cubic units, which we have learnt above by counting the
number of unit cubes.

3
If we take the volume of 1 unit cube as 1 cm , then
3
3
the volume of 72 unit cubes = 72 × 1 cm = 72 cm
\ Volume of the cuboid = 72 cm 3 3 cm 6 cm
4 cm
= 6 cm × 4 cm × 3 cm (multiplying the dimensions)
= length × breadth × height

Thus, the volume of a cuboid = (length × breadth × height) cubic units
If l, b and h are the dimensions of the cuboid, then h
the volume of a cuboid = (l × b × h) cubic units. b
l
activity

Take same rectangular paper sheets of length ‘l’ and breadth ‘b’ and pile one above the other such
that the height of the pile will become h units. Now, the shape will be in the form of a cuboid.

h
b
l

Volume of the cuboid formed = area of a sheet × h
= (l × b) × h
Therefore, Volume of a cuboid = l × b × h
In other words, the Volume of a cuboid = Area of base × height

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