A solid metallic cube of side 20cm is melted and recast into a cuboid of length 40 cm and breadth 40 cm. What is the length (in cm) of the body diagonal of the cuboid?

The cube's volume is 20³ = 8000 cm³. When melted and recast, the cuboid has length 40, breadth 40, and height h such that 40 × 40 × h = 8000, giving h = 5 cm. The body diagonal of a cuboid with dimensions l, b, h is √(l² + b² + h²). Substituting: √(40² + 40² + 5²) = √(1600 + 1600 + 25) = √3225 = √(25 × 129) = 5√129. This applies conservation of volume followed by the 3D Pythagorean theorem.