If we reduce the diameter by 25%, the radius will also be reduced by 25%.
let initial radius of sphere = r
initial CSA = 4πr²
after reducing it 25%,
25% of r = (25/100)×r = 0.25r
final radius = r - 0.25r = 0.75r
final CSA = 4π(0.75r²) = 4πr²×(0.5625)
decrease in CSA = initial CSA - final CSA = 4πr² - 4πr² × (0.5625)
⇒decrease in CSA = 4πr² × (1-0.5625) = 4πr² × 0.4375
% decrease in CSA =
Thus CSA decreases by 43.75%.