The diameter of a sphere is decreased by 25%. By what per cent does it

1.	The diameter of a sphere is decreased by 25%. By what per cent does its curvedsurface area decrease?
Answer» If we reduce the diameter by 25%, the radius will also be reduced by 25%. let initial radius of sphere = rinitialCSA = 4πr² after reducing it25%,25% of r = (25/100)×r = 0.25rfinal radius = r - 0.25r = 0.75rfinalCSA = 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 Thus CSA decreases by 43.75%.

The diameter of a sphere is decreased by 25%. By what per cent does its curvedsurface area decrease?

Answer»

If we reduce the diameter by 25%, the radius will also be reduced by 25%.

let initial radius of sphere = rinitialCSA = 4πr²

after reducing it25%,25% of r = (25/100)×r = 0.25rfinal radius = r - 0.25r = 0.75rfinalCSA = 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

Thus CSA decreases by 43.75%.