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.

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RPF SI (2018) Official Paper (Held On: 24 Dec, 2018 Shift 1)
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  1. 16 cm
  2. 20 cm
  3. 18 cm
  4. 14 cm

Answer (Detailed Solution Below)

Option 3 : 18 cm
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Detailed Solution

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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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