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A cube of diagonal 21√3 is melted and cast into a cuboid. The length of the cuboid is the same as the side of the cube, the width of the cuboid is 10.5 cm, what is the height of the cuboid? (in cm)

A cube of diagonal 21√3 is melted and cast into a cuboid. The length of the cuboid is the same as the side of the cube, the width of the cuboid is 10.5 cm, what is the height of the cuboid? (in cm) Correct Answer 42

Given:

Diagonal of Cube = 21√3

The length of the cuboid = the side of the cube.

The width of the cuboid=  10.5 cm

Concept used:

The volume of  cube = Volume of cuboid.

Formula used:

As we know,

Volume of cube = a3

Volume of cuboid = lbh

Diagonal of the cube = √3 a

Calculation:

Diagonal of the cube = √3 a

⇒ √3 a = 21 √3

⇒ a = 21

Length of the cuboid, l = 21 cm

Let the height of the cuboid be h cm

Width of the cuboid, b = 10.5 cm

According to the question

21 × 10.5 × h = 21 × 21 × 21

⇒ h = (21 × 21 × 21)/(21 × 10.5)

∴ h = 42 cm

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