The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

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#### Solution

Let the diameter of the sphere be *d*.

Radius (*r*_{1}) of sphere = d/2

New radius (r_{2}) of sphere `= d/2(1-25/100)=3/8d`

CSA (*S*_{1}) of sphere `= 4pir_1^2`

`=4pi(d/2)^2=pid^2`

CSA (*S*_{2}) of sphere when radius is decreased`= 4pir_2^2`

`=4pi((3d)/8)^2=9/16pid^2`

Decrease in surface area of sphere = *S*_{1} − *S*_{2}

`=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%`

Concept: Volume of a Sphere

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