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If the cube with a 26√3 cm diagonal is melted then how tall is the height of the cuboid, if the length of the cuboid is equal to the arm of the cube, and the width of the cuboid is 13 cm? (in cm)

If the cube with a 26√3 cm diagonal is melted then how tall is the height of the cuboid, if the length of the cuboid is equal to the arm of the cube, and the width of the cuboid is 13 cm? (in cm) Correct Answer 52

As we know,

The volume of cube = a3

The volume of cuboid = lbh

Diagonal of the cube = √3a

⇒ √3a = 26√3

⇒ a = 26

Length of the cuboid l = 26 cm

Let the height of the cuboid be h cm

Width of the cuboid b = 13 cm

According to the question

26 × 13 × h = 26 × 26 × 26

⇒ h = (26 × 26 × 26) / (26 × 13)

∴ h = 52 cm

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