Question

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

• A. 10
• B. 50
• C. 60
• D. 20

Answer 1

Answer: (B)

50

Answer 2

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.