If the surface area of a sphere S1 is 800% greater than that of sphere S2, and the volume of sphere S2 is x% lower than sphere S1, then ‘x’ in terms of percentage is:
(Rounded off to two places of decimals.)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 96.29%
Given that
If the surface area of sphere S1 is 800% greater than that of sphere S2,
the volume of sphere S2 is x% lower than that of sphere S1
Formula used
Surface Area of Sphere = 4πr²
The volume of a sphere is V = 4/3 π r³
Calculation
4πr1² = 9 × 4πr2²
r1 = 3 r2
So, r13 = (10.39 r2)3 = 27 r23
r23/r13 = 1/27
Now, the % change in volume = [(27 - 1)/27] × 100 = 96.29%