Question

if the diameter of a sphere is decreased by 25% then by what%its curved area would decrease?

Answer 1

Let diameter of sphere = d
radius=d/2, SA=4π×d^2/4=πd^2
diameter decrease by 25%
then, diameter= d-d/4= 3d/4
radius= 3d/8, SA=4π×9d^2/64= 9πd^2/16

decrease SA = πd^2 - 9πd^2/16 = 7πd^2/16
% decrease SA
7πd^2/16
-------------- × 100
πd^2

7/16 × 100

7×25/4
175/4= 43.75%