A spherical balloon is inflated, causing its radius to grow by 10%. By what percentage does its surface area increase?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 21%.
Let the radius = r
Surface area of sphere = 4πr2
Area ∝ Radius2
Radius increases by 10% ⇒ New radius = 1.1r
New area = (1.1)2 × Old area = 1.21 × Old area
Increase = 1.21 – 1 = 0.21
Increase percentage = 0.21 × 100 = 21%