A spherical balloon with radius r inches has volume V(r) = (4/3)πr^3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 1 inches. (Express your answer in terms of π and r.)

Question

A spherical balloon with radius r inches has volume  V(r) = (4/3)πr^3.  Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 1 inches. (Express your answer in terms of π and r.)

anonymous · Answer

I think I might have figured it out:
$$V(r+1)-V(r)=(4/3)\pi(r+1)^3-(4/3)pir^3$$
$$=(4/3)\pi((r+1)^3-r^3)$$
$$=(4/3)\pi(r^3+3r^2+3r+1-r^3)$$
$$=(4/3)\pi(3r^2+3r+1)$$

Would there be anything else I would have to do to this then? Thanks in advance.