Question

the radius of a sphere is increased 10%.the surface area increase by

Answer 1

from net effect formula
x +y + (xy)/100
x = 10 and y = 10
i am taking same value 2 time because of the surface area formula A = 4πr^2
here r is 2 times so we take two times radius.
10+10+(10×10)/100
= 20+1 = 21%
so increased area = 21%
method 2
radius increased 10%.
10% means 1/10
it means initially radius was 10 but after increment of 10% it became 11.
so when radius was 10
then area = 4 π 10×10= 400π
now, when radius became 11 then new area = 4π × 11×11= 484π
so it is clear that old area = 400π, new area = 484π
so % increase area between these two area =
[(484π - 400π)/400π] × 100
= 84π/4π = 21%
so increase = 21%