Question

A cuboid is of dimensions 60 cm x 54 cm x 30 cm. How many small cubes with
sides 6 cm can be placed in the given cuboid . With step by step explanation
​

Answer 1

Answer:

Number of cubes which can be placed in given cuboid is 450.

Step-by-step explanation:

Given :-

• Dimensions of cuboid are 60 cm x 54 cm x 30 cm.
• Side(edge) of small cube is 6 cm.

To find :-

• Number of small cubes which can be placed in the given cuboid.

Solution :-

• Here, If we want to place small cubes in cuboid then first we need to know volume of cuboid and volume of cubes.

So,

We know,

Volume of cuboid = lbh

[l is length, b is breadth and h is height of cuboid]

l = 60 cm

b = 54 cm

h = 30 cm

Put all values in formula :

$\longrightarrow$ Volume = 60 × 54 × 30

$\longrightarrow$ Volume = 97200

Volume of cuboid is 97200 cm³.

And,

Volume of cube = (edge)³

Edge = 6 cm

Put edge in formula :

$\longrightarrow$ Volume = (6)³

$\longrightarrow$ Volume = 216

Volume of one small cube is 216 cm³.

Now,

$\sf Number \: of \: cubes = \dfrac{Volume \: of \: cuboid}{Volume \: of \: one \: cube}$

$\leadsto$ 97200/216

$\leadsto$ 450

$\bold{\therefore}$ Number of cubes which can be placed in given cuboid is 450.

Answer 2

Answer:

Given :-

• A cuboid is of dimensions 60 cm × 54 cm × 30 cm.

To Find :-

• How many small cubes with sides 6 cm can be placed.

Formula Used :-

$\sf\boxed{\bold{\pink{Volume\: of\: Cuboid =\: Length \times Breadth \times Height}}}$

$\sf\boxed{\bold{\pink{Volume\: of\: Cube =\: {(Side)}^{3}}}}$

Solution :-

First, we have to find the volume of cuboid,

Given :

• Length = 60 cm
• Breadth = 54 cm
• Height = 30 cm

Then, according to the question by using the formula we get,

⇒ $\sf Volume\: of\: Cuboid =\: 60 \times 54 \times 30$

⇒ $\sf Volume\: of\: Cuboid =\: 3240 \times 30$

➠ $\sf\bold{\green{Volume\: of\: Cuboid =\: 97200\: {cm}^{3}}}$

Hence, the volume of cuboid is 97200 cm³.

Again, we have to find the volume of cube,

Given :

• Side = 6 cm

According to the question by using the formula we get,

↦ $\sf Volume\: of\: Cube =\: {(6)}^{3}$

↦ $\sf Volume\: of\: Cube =\: 6 \times 6 \times 6$

➦ $\sf\bold{\purple{Volume\: of\: Cube =\: 216\: {cm}^{3}}}$

Hence, the volume of cube is 216 cm³.

Now, we have to find the how many small cubes needed,

Again, we know that,

$\sf\boxed{\bold{\pink{Required\: Number\: of\: Cubes =\: \dfrac{Volume\: of\: the\: Cuboid}{Volume\: of\: the\: small\: cube}}}}$

Given :

• Volume of the cuboid = 97200 cm³
• Volume of the small cube = 216 cm³

According to the question by using the formula we get,

↬ $\sf Required\: Number\: of\: Cubes =\: \dfrac{\cancel{97200}}{\cancel{216}}$

➲ $\sf\bold{\red{Required\: Number\: of\: Cubes =\: 450}}$

$\therefore$ 450 small cubes can be placed in the given cuboid.