Question

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

Answer 1

old csa=4pi r2
increase in radius=25 percent
new radius =125r/100
new csa =4pi 125r/100×125r/100=4pi 15625/10000
increase in csa =5625r2/10000
increase in csa percent=100×5625r2/10000r2=56.25
There fore it will increase 56.25percent

Answer 2

Answer:

CSA decreases by 43.75%.

Explanation:

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

let the 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%.

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