A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 7 : 8.
In this case, the volume remains constant.
The volume of cuboid = volume of 8 cubes.
18 × 36 × 72 = 8 × a3
a = 18.
Total surface area of cuboid = 2(18 × 36 + 36 × 72 + 72 × 18) = 2(648 + 2592 + 1296)
= 9072cm2
LSA of cube = 8 × 4 × 18 × 18 = 10368cm2.
Required ratio = 9072 : 10368 = 7 : 8.