Question

a cuboid is of 60 cm × 54 cm × 30 cm. how many cubes with the side 6 cm can be placed in a given cube.

Answer 1

Volume of cuboid = lbh
= 60×54×30
=97200cm^3
Now,
Volume of cube = (side)^3
=6×6×6
=216 cm^3

Then, no of cubes that can fit inside the cuboid
=97200÷216
=450 cubes

Answer 2

Given:

• Length of the cuboid = 60 cm
• Breadth of the cuboid = 54 cm
• Height of the cuboid = 30 cm
• Length of each side of a cube = 6 cm

To Find:

The number of cubes with the side 6 cm which can be placed in the given cube.

Solution:

As per the given information,

Length of the cuboid = 60 cm, Breadth = 54 cm, Height = 30 cm

We know that,

Volume of a cuboid = lbh

Finding the volume,

60 × 54 × 30 (Substituting the values)

$:\implies \boxed{97200 \: cm^{3} }$

Now, finding the volume of the cube,

Volume of a cube = $(Side)^{3}$

$:\implies 6 \times 6 \times 6 = 216 \: cm^{3}$

Finding the required cubes that need to be placed,

Number of small cubes = $\frac{Volume \: of \: cuboid}{Volume \: of \: cube}$

$:\implies \frac{97200}{216}$

$:\implies \boxed{Required \: cubes \: are \: 450}$

Hence, 450 number of cubes required to be placed.