Rates of change in the natural and social sciences

[elindow]

That was just the name of the section...the problem states this:

A sphrerical balloon is being inflated. Find the rate of increase of the surface area (S=4*Pi*r²) with respect to the radius r when r is (a) 1 ft, (b) 2 ft, and (c) 3 ft. What conclusion can you make?

well when I work the problem I am getting about half of what I should. Example on part a I am getting 4*Pi ft² instead of 8*Pi ft².

Can someone please help?

Thanks
Erik

 

[Gene]

Well, dS/dr=8PI*r which is what you are looking for but you don't seem to be using calculus. How about:
S=4PI*r²
If r changes by a
then S changes by b so
S+b=4PI(r+a)² =
4PIr²+8PIra+4PIa²
Subtracting
b=8PIra+4PIa²
b/a=8PI*r if a is very small so 4PIa can be ignored.