A solid metallic cube of side 20 cm 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?

$5\sqrt{129}$

We know that,

Volume of cube = (side)³ 

Volume of cuboid = l × b × h 

Diagonal of cuboid =  \(\sqrt { l^2 + b^2 + h^2 }\)

So,

Volume of cube = Volume of cuboid 

= 20 × 20 × 20 = 40 × 40 × h

= h = (20 × 20 × 20) × \(\frac{1}{1600}\)

= h = 5 cm 

Diagonal of the cuboid = \(\sqrt {40^2 + 40^2 + 5^2 }\)

= \(\sqrt {1600 + 1600 + 25 }\)= \(\sqrt {3325 }\)

= 5\(\sqrt {129}\) cm