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.

Question

Question

This question was previously asked in

RPF SI (2018) Official Paper (Held On: 24 Dec, 2018 Shift 1)

Answer 1

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.

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