Question

if the radius of a sphere decreases by 0.1%,find the percentage decreases in (i)surface area
(ii)volume

Answer 1

for area, our new area is

4pi(.99r)^2
So, if we divide that by the original area, we have

4pi(.99r)^2 / 4pir^2 = .99^2

1-.99^2 = 0.0199

That is, a 1.99% decrease in area

Note that the area decreases by about twice the percentage as the radius.

I think you can expect the volume to decrease by about 3 times the %age of the radius.