If a cube of diagonal 9√3 cm is melted to form a cuboid, what will be its height, if the length of the cuboid is equal to the side of the cube and the width of the cuboid is 4.5 cm.

Given:

Diagonal of the cube = 9√3 cm

Width of the cuboid = 4.5 cm

Length of the cuboid = Side of the cube

Formula Used:

Diagonal of the cube = Side × √3

Volume of the cube = Side³

Volume of the cuboid = Length × Width × Height

Calculation:

Let the side of the cube be a cm.

Diagonal of the cube = a√3

Given, Diagonal of the cube = 9√3 cm

⇒ a√3 = 9√3

⇒ a = 9 cm

Volume of the cube = a³

⇒ Volume of the cube = 9³

⇒ Volume of the cube = 729 cm³

Let the height of the cuboid be h cm.

Volume of the cuboid = Length × Width × Height

⇒ Volume of the cuboid = 9 × 4.5 × h

Since the cube is melted to form the cuboid, their volumes will be equal.

⇒ 729 = 9 × 4.5 × h

⇒ 729 = 40.5 × h

⇒ h = 729 / 40.5

⇒ h = 18 cm

The height of the cuboid is 18 cm.