Question

The diameter of a sphere is decreased by 20% . By what percentage does its curved surface area decreases or increases ?

Answer 1

Let the diameter of sphere be "d"

curved surface area of sphere = 4πr2

= π (2r)2

= π(d)2

Given diameter of sphere decreases by 20%

New diameter = d - (d/5) = 4d/5

New curved surface area = π(4d/5)2

                   = (16/25) πd2

Change in surface area of sphere = πd2 – (16/25) πd2

= (9/25) πd2

decrease in curved surface area = [9/25) πd2/ πd2] x 100 = 36%

Therefore surface area decreases by 36%

Answer 2

Original D=D° New D=D1 Since diameter is decreased by 20% D1= D-D/5= 4/5 D  Curved surface are of sphere = 4 pi (D/2)^2  New curved suface area = 4 pi (4/5*D/2)^2  Percentage decrease = (4/5)^2 =16/25