Question

A cuboid is of dimensions 60cm, 54 cm, 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Answer 1

Hint: The volume of the cuboid into which cubes is to be placed is obviously larger than the volume of the cube which is to be placed inside. Division of these volumes will tell about the total number of cubes that can be fitted.

Complete step-by-step answer:

Given dimensions of the cuboid is
Length (l) = 60 cm
Breadth (b) = 54 cm
Height (h) = 30 cm
As we know that the volume (Vcuboid) of the cuboid is $ = l.b.h$
$ \Rightarrow {V_{cuboid}} = 60 \times 54 \times 30{\text{ c}}{{\text{m}}^3}$
Now it is given that the side of the cube is 6 cm.
Now as we know that the volume (Vcube) of the cube is $ = {\left( {{\text{side}}} \right)^3}$.
$ \Rightarrow {V_{cube}} = {6^3}{\text{ c}}{{\text{m}}^3}$.
Now we have to find out how many small cubes with side 6 cm can be placed in the given cuboid.
So in order to find out the number of small cubes (S.C) we have to divide the volume of cuboid to the volume of the cube.
$ \Rightarrow S.C = \dfrac{{{V_{cuboid}}}}{{{V_{cube}}}} = \dfrac{{60 \times 54 \times 30}}{{6 \times 6 \times 6}} = 10 \times 9 \times 5 = 450$.
Therefore 450 small cubes are placed in the given cuboid.
So this is the required answer.

Note: Whenever we face such types of problems the key concept is simply to have a good understanding of the direct formula of the basic shapes like cuboid and cube as it helps simplify the problems and save a lot of time.