# The diameter of a sphere is decreased by 25%.by what % does it's curved surface area decrease ?

2
by manasmitabera

2015-02-28T18:16:35+05:30

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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%.
2015-02-28T18:26:01+05:30

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