Question

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

Answer 1

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%