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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 5
Volume of cube = (side)3
Volume of cuboid = l × b × h
Diagonal of cuboid = √ l2 + b2 + h2
Volume of the cube = Volume of the cuboid
⇒ 20 × 20 × 20 = 40 × 40 × h
⇒ h = (20 × 20 × 20) ÷ (40 × 40)
⇒ h = 5 cm
Diagonal of the cuboid = √ 402 + 402 + 52
⇒ √ 1600 + 1600 + 25 = √ 3225
⇒ 5√129 cm