Question

 A hollow cuboid is of dimensions 72 m X 48 m X 24 m. How many small cubes of 12 m can be placed in the cuboid.​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, we are given that the dimensions of the cuboid are 72 m, 48 m and 24 m. We have to find the number of small cubes of 12 m that can be placed in the cuboid.

We'll assume the number of required cubes as a variable, say 'x'. Here, we need to calculate he volume or capacity of the hollow cuboid first. After that, we'll calculate the volume of one small cube. Then, by forming a linear equation & solving that equation ; we'll find the number of required cubes.

$\Large {\underline { \sf \orange{Explication \: of \: steps :}}}$

Let, the number of small cubes of 12 m that can be placed in the cuboid as x. So,

$\bigstar \: \boxed{\sf { Number_{(Cubes)} \times Volume_{(One \: Cube)}= Volume_{(Cuboid)} }}$

$\bf \red {\dag }$ Volume of small cube :

We know that,

$\bigstar \: \boxed{\sf { Volume_{(Cube)} = {(Side)}^{3} }}$

• Side = 12 m

$\longrightarrow \sf { Volume_{(Cube)} = {(12 \: m)}^{3} }$

$\longrightarrow \sf { Volume_{(Cube)} = 1728 \: {m}^{3} }$

$\bf \red {\dag }$ Volume of cuboid :

We know that,

$\bigstar \: \boxed{\sf { Volume_{(Cuboid)} = \ell \times b \times h}}$

• Length = 72 m
• Breadth = 48 m
• Height = 24 m

$\longrightarrow \sf{Volume_{(Cuboid)} = 72 \: m \times 48 \: m \times 24 \: m }$

$\longrightarrow \sf{Volume_{(Cuboid)} = 82944 \: {m}^{3} }$

$\bf \red {\dag }$ Required number of cubes :

$\bigstar \: \boxed{\sf { Number_{(Cubes)} \times Volume_{(One \: Cube)}= Volume_{(Cuboid)} }}$

$\longrightarrow \sf {x \times Volume_{(One \: Cube)}= Volume_{(Cuboid)} }$

$\longrightarrow \sf {x=\dfrac{ Volume_{(Cuboid)} }{ Volume_{(One \: Cube)}} }$

$\longrightarrow \sf {x=\cancel{\dfrac{ 82944 \: {m}^{3}}{ 1728 \: {m}^{3}} }}$

$\longrightarrow \sf {x = 48 }$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { Number_{(Cubes)} = 48 \: cubes}}$ ❞

❝ Therefore, $\pmb { \mathfrak \gray{ 48\: cubes} }$ of 12 m can be placed in the cuboid.❞

Answer 2

Given :

Dimensions of Cuboid :

• Length = 72m
• Breadth = 48m
• Height = 24m

Dimensions of Cube :

• Side of Cube = 12m

To Find :

• How many small cubes of 12 m can be placed in the cuboid.

Solution :

✰ As we know that, Volume of Cuboid is given by Length × Breadth × Height and Volume of Cube is given by (side)³ or side × side × side. Now in this question, we have to find that how many small cubes of 12m can be made from a cuboid of length 72m, breadth 48m, and height 24m. So for finding the number of cubes that can be placed into the cuboid, we will find the volume of Cuboid and cube seperately and then we will divide them to find the number of cubes that can be made from it.

⠀

⠀⟼ ⠀Volume of Cuboid = L × B × H

⠀⟼ ⠀Volume of Cuboid = 72 × 48 × 24

⠀⟼ ⠀Volume of Cuboid = 72 × 1152

⟼ ⠀Volume of Cuboid = 82,944m³..(1)

⠀

Now,

⟼ ⠀Volume of Cube = (side)³

⟼ ⠀Volume of Cube = side × side × side

⟼ ⠀Volume of Cube = 12 × 12 × 12

⟼ ⠀Volume of Cube = 12 × 144

⟼ ⠀Volume of Cube = 1,728m³...(2)

⠀

So,

⟹ Number of Cubes = (1) / (2)

⟹ Number of Cubes = 82944/1728

⟹ Number of Cubes = 48 cubes.

Thus 48 cubes can be placed in the cuboid.

________________