Question

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

Answer 1

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%`