Multiple choice

Directions: Solve the following question and mark the best possible option. A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to

  1. 10

  2. 50

  3. 60

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original volume be V. The five cubes have volumes V/40, V/40, 8V/40, 27V/40, 27V/40 (summing to V). Calculating the surface areas (proportional to volume^(2/3)) and comparing the sum to the original cube's surface area shows an increase of approximately 50%.

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