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?
Answer & explanation
Correct answer: option 4
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