If the radius of a sphere is decreased by 25%, then the percentage decrease in its surface area is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 43.75.
Let the original radius of sphere be r.
New radius = r - 25% of r = 0.75r
Original surface area of sphere = 4πr2
New surface area of sphere = 4π(0.75r)2 = 4π(0.5625r2)
Percentage decrease in area = [(4πr2 - 4π(0.5625)r2) × 100]/4πr2 = 0.4375(100) = 43.75%