Question

Find the percentage decrease in the curved surface area of a sphere of its diameter is decreased by 25 percent
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Answer 1

CSA of sphere =4πr² = πd²
if diameter is decreased by 25%,
new diameter = d - 0.25d = 0.75d 

final CSA = π(0.75d)² = 0.5625 πd²

decrease in CSA = πd² - 0.5625 πd² = 0.4375 πd²
%  decrease = (0.4375 πd² / πd² ) ×100 = 43.75%

Answer 2

let diameter be 2x
then radius will be x

older C.S.A.= 4πr²
                 =4πx²
when diameter is decreased by 25%
new diameter 2x - 2x * 25/100
                   2x - x/2
                   =3x/2
new radius = 3x / 2* 1/2
                 3x/4
new C.S.A.= 4π(3x/4)²
                 4π9x²/16
                =9πx²/4
increase n S.A. = 4πx²- 9πx²/4
                    =πx²(4-9/4)
                    =πx²7/4

                           7πx²  X 100                7 X 25
 % increaed  =     -----------------------  =   ------------------- =  43.75%
                             4πx² X 4                    4