Question

If the diameter of a sphere is decreased by 25%,

then by what percent its curved area would

decrease

Answer 1

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 %