Question

the side of the metallic cube is 12 cm it is melted and formed into a cuboid whose length and breadth are 18 cm and 16 respectively find the height of a cuboid? ​

Answer 1

Step-by-step explanation:

A metal cube of side 12 cm. is melted and a cuboid whose length is 18 cm. and breadth 16 cm. is formed. Then, the height of the cube is 6 cm.

Answer 2

Given :-

Side of the cube = 12 cm

Length of the cuboid = 18 cm

Breadth of the cube = 16 cm

To Find :-

Height of the metallic cuboid.

Analysis :-

Using the formula find the volume of the cube.

Consider the height as a variable and substitute it in the formula of volume of a cuboid.

Solution :-

We know that,

• s = Side
• l = Length
• b = Breadth
• h = Height

Since the cube is melted to form a cuboid, the volume of cube will be same of cuboid.

Given that, side = 12 cm

By the formula,

$\underline{\boxed{\sf Volume \ of \ a \ cube=(side)^{3}}}$

Substituting their values,

Volume = 12³

Volume = 1728 cm³

Therefore, volume of the cube is 1728 cm³

Let us consider the height to be 'h'

Given that,

Length = 18 cm

Breadth = 16 cm

By the formula,

$\underline{\boxed{\sf Volume \ of \ a \ cuboid=Length \times Breadth \times Height}}$

Substituting their values,

$\sf 1728=18 \times 16 \times h$

$\sf 1728=288h$

$\sf h=\dfrac{1728}{228}$

$\sf h=6$

Therefore, the height of the cuboid is 6 cm