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What would be the height of the cuboid framed from melting the cube and the length of the cuboid is equal to the arm of the cube whose diagonal is 28√3 and the width of the cuboid is 14 cm. (in cm)

What would be the height of the cuboid framed from melting the cube and the length of the cuboid is equal to the arm of the cube whose diagonal is 28√3 and the width of the cuboid is 14 cm. (in cm) Correct Answer 56

As we know,

Volume of cube = a3

Volume of cuboid = lbh

Diagonal of the cube = √3a

⇒ √3a = 28√3

⇒ a = 28

Length of the cuboid l = 28 cm

Let height of the cuboid be h cm

Width of the cuboid b = 14 cm

According to the question

⇒ 28 × 14 × h = 28 × 28 × 28

⇒ h = (28 × 28 × 28)/(28 × 14)

⇒ h = 56 cm

∴ height of cuboid is 56 cm

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