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Question
The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?
Solution
Let the diameter of the sphere be d.
Radius (r1) of sphere = d/2
New radius (r2) of sphere `= d/2(1-25/100)=3/8d`
CSA (S1) of sphere `= 4pir_1^2`
`=4pi(d/2)^2=pid^2`
CSA (S2) of sphere when radius is decreased`= 4pir_2^2`
`=4pi((3d)/8)^2=9/16pid^2`
Decrease in surface area of sphere = S1 − S2
`=pid^2-9/16pid^2`
`=7/16pid^2`
`"Percentage decrease in surface area of sphere "=(S_1-S_2)/S_1xx100`
`= (7pid^2)/(16pid^2)xx100=700/16=43.75%`
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