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What is the height of the cuboid, if the cube of diagonal 19√3 cm is melted and casted, the cuboid’s length is the same as the cube’s side and the breadth of the cuboid is 9.5 cm?

What is the height of the cuboid, if the cube of diagonal 19√3 cm is melted and casted, the cuboid’s length is the same as the cube’s side and the breadth of the cuboid is 9.5 cm? Correct Answer 38 cm

As we know,

Volume of cube = a3

Volume of cuboid = length × breadth × height

Diagonal of the cube = √3 a

⇒ √3a = 19√3

⇒ a = 19

Length of the cuboid = 19 cm

Let height of the cuboid be h cm

Width of the cuboid b = 9.5 cm

When any shape is casted to another shape then their volume remain same

⇒ 19 × 9.5 × h = 19 × 19 × 19

⇒ h = (19 × 19 × 19)/(19 × 9.5)

⇒ h = 38 cm

∴ Height of cuboid so formed by melting will be 38 cm

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