If a cube with diagonal 7√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 3.5 cm.

Given:

A cube with a diagonal of 7√3 cm is melted to form a cuboid. The length of the cuboid is equal to the side of the cube, and the width of the cuboid is 3.5 cm.

Concept:

The diagonal of a cube is given by the formula: d = a√3, where 'a' is the side of the cube.

The volume of the cube is equal to the volume of the cuboid formed.

Formula Used:

Diagonal of cube: d = a√3

Volume of cube: V = a³

Volume of cuboid: V = l × w × h

Calculation:

We have,

⇒ Diagonal of cube = 7√3 cm

⇒ a√3 = 7√3

⇒ a = 7 cm

Volume of the cube:

⇒ V = a³

⇒ V = 7³

⇒ V = 343 cm³

Volume of the cuboid:

⇒ V = l × w × h

⇒ 343 = 7 × 3.5 × h

⇒ 343 = 24.5h

⇒ h = 343 / 24.5

⇒ h = 14 cm

∴ The height of the cuboid is 14 cm.