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

 Solution:

Let the diameter of the sphere be “d”.

Radius of sphere, r1 = d/2

New radius of sphere, say r2 = (d/2)×(1-25/100) = 3d/8

Curved surface area of sphere, (CSA)1 = 4πr12 = 4π×(d/2)2 = πd2 …(1)

Curved surface area of sphere when radius is decreased (CSA)2 = 4πr22 = 4π×(3d/8)2 = (9/16)πd2 …(2)

From equation (1) and (2), we have

Decrease in surface area of sphere = (CSA)1 – (CSA)2

= πd2 – (9/16)πd2

= (7/16)πd2

= (7d2/16d2)×100 = 700/16 = 43.75% .

Therefore, the percentage decrease in the surface area of the spher