# Find the percentage decrease in the curved surface area of a sphere of its diameter is decreased by 25 percent plzzzzzzz DO AS FAST AS U CAN PLZZZZZZZZZZZZZZ

2
by Deleted account

2015-03-05T23:05:39+05:30

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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%
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take πd² common
πd² - 0.5625 πd² = πd²(1-0.5625) =πd² * 0.4375 = 0.4375 πd²
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2015-03-06T05:14:08+05:30

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let diameter be 2x

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