Question

the diameter of sphere is decreased by 25% by what percentage will its surface area decrease

Answer 1

Let the Diameter of sphere be a
Radius of sphere = a/2
Surface Area = 4 *pi *r^2
= 4*pi *a^2 /4
= pi *a^2

Diameter of new sphere = a - 25a/100
= 3a/4
Radius = 3a/8
Surface Area = 4 pi *9a^2 /64
= pi * 9a^2 /16

Decrease in Surface Area = pi a^2 - pi a^2 *9/16
= pi *a^2 (1-9/16)
= pi a^2 *7/16

% of Decrease in Area =( pi a^2 *7/16) *100/pi *a^2
= 7*100/16
= 7* 25/4
= 175 /4
= 43.75 %