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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 =  \frac{decrease\ in\ CSA}{initial\ CSA} \times 100= \frac{0.4375 \times 4 \pi r^2}{4 \pi r^2} \times100=43.75

Thus CSA decreases by 43.75%.
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2015-02-28T18:26:01+05:30

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Let the initial radius be=r
On decreasing by 25%,new radius=r-((25/100)xr)=3r/4
Initial surface area=4πr²
Final surface area=4π(3r/4)²=4π9r/16
% of new surface area=56.25%
% of decrease in area=(100-56.25)%=43.75%
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