The diameter of a sphere is decreased by 25% by what per cent does cuverd surface area decrease?
raoatchut191:
hope the ans is 625/4 %
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diameter becomes (100% - 25%) = 75% of its previous value = 0.75D = 3D/4
curved surface area of a sphere = 4π R² / 3 => π D² / 3
new surface area = (π/3) (3D/4)² / 3
= 9/16 * πD²/3
reduction in surface area = πD²/3 - 9/16 * πD²/3
= 7/16 * πD²/3
% decrease = 7/16 * 100 = 43.75%
curved surface area of a sphere = 4π R² / 3 => π D² / 3
new surface area = (π/3) (3D/4)² / 3
= 9/16 * πD²/3
reduction in surface area = πD²/3 - 9/16 * πD²/3
= 7/16 * πD²/3
% decrease = 7/16 * 100 = 43.75%
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