Question 18: 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

10

50

60

20

Option: 2 Explanation: The volumes of the 5 smaller cubes and the
original big one are in the ratio 1 : 1 : 8 : 27 : 27
: 64. Therefore, the sides are in the ratio 1 : 1 : 2
: 3 : 3 : 4 while the areas are in the ratio 1 : 1 : 4
: 9 : 9 : 16. The sum of the areas of the 5
smaller cubes is 24 parts while that of the big
cube is 16 parts. The sum is 50% greater.