In need of help on a calculus problem!?

Question

A spherical balloon with radius r inches has volume V(r) = (4/3)πr3. Find a function that represents the amount of air A required to inflate the balloon from a radius of r inches to a radius of r + 1 inches.

Where I am at so far:

I replaced r with (r+1) and came up with A(r)=(4/3)π(r+1)^3

Now I have read that you are supposed to take the difference of them but...that's where I'm beginning to run into problems.

A(r)= (4/3)π(r+1)^3 - (4/3)πr^3

= (4/3)π((r+1)^3-r^3)

=(4/3)π((r^3+3r62=3r+1)-r^3)

=(4/3)π(3r^2+3r+1)

And that's about as far as I've got, but I don't even know if I am going down the right path. Any help?

Answer 1

It seems correct and complete to me.  Like if you go from 5 to 6, it goes from 125 to 216; 216 - 125 = 91 and 3(5^2) + 3(5) + 1 = 91