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Question

Question 3
The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

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Solution

Let the diameter of the sphere be d.
Radius (r1) of the sphere =d2
New radius, (r2) of the sphere =d2(125100)=38d
CSA (S1) of sphere =4πr21
=4π(d2)2=πd2
CSA (S2) of the sphere when radius is decreased =4πr22
=4π(3d8)2=916πd2
Decrease in the surface area of the sphere =S1S2
=πd2916πd2=716πd2
Percentage decrease in the surface area of the sphere =S1S2S1×100
=7πd216πd2×100=70016=43.75%

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