CAT 2003 Slot 1 — QA Question 7
SphereEasy
Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be
Answer & solution
Correct answer: 87.5
- A
85.5
- B
92.5
- C
90.5
87.5
Solution
Ratio of areas of two spheres = s1 : s2 = 4 : 1
∴ Ratio of their radii = r1 : r2 = 2 : 1
∴ Ratio of their volumes = v1 : v2 = 8 : 1
Volume of A is 12.5% (1/8th) of the volume of B.
But, volume of A is k% less than B.
∴ k = (100 − 12.5) = 87.5%
Hence, option (d).