Question

4. A cuboid is of dimensions 60 cm x 54 cm x 30 cm. How many small cubes with side
6 cm can be placed in the cuibod?​

Answer 1

Answer:

Given :-

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

To Find :-

• How many small cubes with side 6 cm can be placed in the cuboid.

Formula Used :-

${\red{\boxed{\small{\bold{Volume\: of\: Cuboid =\: L \times B \times H}}}}}$

where,

• L = Length
• B = Breadth
• H = Height

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

Solution :-

First we have to find the volume of cuboid,

Given :

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

According to the question by using the formula we get,

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

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

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

Again we have to find the volume of cube,

Given :

• Side = 6 cm

According to the question by using the formula we get,

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

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

➤ $\sf\bold{\pink{Volume\: of\: Cube =\: 216\: {cm}^{3}}}$

Now we have to find how many small cubes can be placed in the cuboid,

As we know that,

$\sf Number\: of\: Cubes =\: \dfrac{Volume\: of\: Cuboid}{Volume\: of\: Cube}$

Given :

• Volume of Cuboid = 97200 cm³
• Volume of Cube = 216 cm³

According to the question by using the formula we get,

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

➠ $\sf\bold{\purple{Number\: of\: Cubes =\: 450}}$

$\therefore$ 450 is the required number of small cubes with side 6 cm can be placed in the cuboid.

Answer 2

Answer:

Given :-

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

To Find :-

Total 6 cm cube can fixed

Solution :-

We know that

Volume of cuboid = L × B × H

Volume = 60 × 54 × 30

Volume = 1800 × 54

Volume = 97200 cm³

Now,

Volume of cube = edge³

Volume = 6³

Volume = 216 cm³

Now,

Total cubes = 97,200/216

Total cubes = 450