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Example 26: Find the volume of a cuboid having dimensions 8 cm × 3 cm × 2 cm.

Solution: We have, volume of a cuboid = l × b × h
Here, length = 8 cm, breadth = 3 cm, and height = 2 cm
3 cm 2 cm
Therefore, the volume of given cuboid = 8 cm × 3 cm × 2 cm = 48 cm 3
8 cm
3
2
Example 27: Find the height of a cuboid whose volume is 256 cm and the base area is 32 cm .
Solution: Let the height of the given cuboid be h.

We have, the volume of a cuboid = Area of the base × height
3
2
256 cm = 32 cm × h
256
h = cm = 8 cm
32
Thus, the height of the cuboid = 8 cm.

Volume of a Cube

We know that a cube is a special type of cuboid whose length, breadth and height are the same,
that is, l = b = h = a

Therefore, the volume of a cube = l × b × h

= a × a × a = a cubic units a
3
a
3
Thus, the volume of a cube = a cubic units. a
Example 28: Find the volume of a cube having a side 1.5 cm.
Solution: We have, the volume of a cube = a 3

Here, side, a = 1.5 cm
3
\ Volume of the given cube = 1.5 cm × 1.5 cm × 1.5 cm = 3.375 cm .
Example 29: A cuboidal box is of dimensions 120 cm × 108 cm × 60 cm. How many small cubical
boxes with side 12 cm can be placed in the given cuboidal box?

Solution: Let us first, find the volume of the cuboidal box.
Volume of the cuboidal box = Length × breadth × height

= 120 × 108 × 60 cm 3 Maths Talk
Mr. Bhushan’s bakery sells
Also, the volume of the small cubical box biscuits. For packing purposes, they

3
3
= (side) = (12) cm 3 use cuboidal boxes of the following
dimensions.
Now, the number of small cubical boxes that can be placed Box A: 3 cm × 8 cm × 20 cm.
in the cuboidal box Box B: 4 cm × 12 cm × 10 cm.
= (Volume of cuboidal box) ÷ (Volume of cubical box) Which size of the box will be
economical for the company? Why?
×
120 × 108 60
= = 450 Can you suggest any other size
×
12 × 12 12 (dimensions) that have the same
So, 450 small cubical boxes can be placed in the big cuboidal volume but more economical than
box. these? Discuss with your teacher.

251 Mensuration