If the surface area of a sphere increases by 21%, by what percentage does its volume increase?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 33.1%.
Let radius = r
Surface area ∝ r2
If surface area increases by 21%, new area = 1.21 × Old area
⇒ New radius2 = 1.21r2
⇒ Radius = 1.1r
Volume ∝ r3
New volume = (1.1)3 = 1.331 × Old volume
⇒ Increase = (1.331 - 1) × 100 = 0.331 × 100 = 33.1%