Question

The solid cube with each 12 m is melted and recast into identical solid cuboid, each with length 6m , breadth 4 m and height 2m . Find the number of solid cuboids formed.

Answer 1

Concept:-

Here, A solid cube is melted and recast into identical solid cuboids. To find number of solid cuboids formed we follow the bellow steps.

Given:-

• Side of Solid Cube is 12 m.
• Dimension of Cuboids is 6 m × 4 m × 2 m.

To Find:-

• The number of solid cuboids formed ?

Solution:-

Here, Side of the Solid cube is 12 m.

$\sf{So,\ Volume\ of\ Solid\ Cube\ =\ (Side)^{3}}$

$\sf{\Longrightarrow (12)^{3}}$

$\sf{\Longrightarrow 12 \times 12 \times 12}$

$\sf{\Longrightarrow 1728\ m^{3}}$

Now, Dimension of Solid Cuboid is 6 m × 4 m × 2 m.

$\sf{So,\ Volume\ of\ Solid\ Cuboid\ =\ L \times B \times H}$

$\sf{\Longrightarrow 6 \times 4 \times 2}$

$\sf{\Longrightarrow 48\ m^{3}}$

$\sf{Since,\ Number\ of\ Solid\ cuboids\ =\ \dfrac{Volume\ of\ Cube}{Volume\ of\ Cuboid}}$

                                                 $\sf{= \dfrac{1728}{48}}$

                                                 $\sf{= 36}$

$\sf{Hence,\ Number\ of\ solid\ cuboids\ formed\ is\ 36.}$