CAT 2017 Slot 1 — QA Question 18
Basics of Mensuration/PrismEasy
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:
Answer & solution
- A
10
50
- C
60
- D
20
Solution
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.
Hence, option (b).