A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio (1: 1 : 8: 27: 27). What is the respective ratio of the total surface area of given five cubes to the surface area of the formed cube?
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3 : 4
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4 : 3
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3 : 2
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2 : 3
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None of these
C
Correct answer
Explanation
When a cube is melted and recast, volume is conserved. The side lengths of cubes are proportional to the cube root of their volumes. Given volume ratio 1:1:8:27:27, the side ratio is 1:1:2:3:3. Surface area of a cube is proportional to the square of its side. Summing the surface areas of all five cubes and comparing to the original cube's surface area yields the ratio 3:2.