Question

if radius of a sphere is decreased by 5% then by what percentage will it surface area decrease

Answer 1

Answer:

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Answer 2

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So let the diameter of the sphere be d so radius = d/2 

so curved surface area = 4πd²/4 = πd² unit²

so the diameter is reduced by 25 % so new diameter = d x 75/100 = 3d/4 

so new radius = 3d/8  

so new surface area = 4. π. 9d²/64 = 9πd²/16 unit²

so the percentage difference = 9πd²/16/πd² x 100 = 9/16 x 100 = 225/4 = 56.25 %

so total decrease = 100 - 56.25 = 43.75 %

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