A cuboid of sides 9 cm, 7 cm and 24 cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to that of the cube?
Answer & explanation
Correct answer: option 3
Sides of a cuboid = 9 cm, 27 cm and 24 cm
Total surface area of cuboid, = 2(9 × 27 + 27 × 24 + 24 × 9) = 2(243 + 648 + 216) = 2214cm2
Volume of cuboid, = 9 × 27 × 24 = 5832 cm3.
Let, side of cube = s cm
According to problem,
= s3 = 5832
= s = 18
Side of cube = 18 cm
Total surface area of cube, = 6 × 182 = 1944
Required ratio, = 2214 ∶ 1944 = 41 ∶ 36