## anonymous 5 years ago A spherical balloon with radius r inches has volume defined by the function below. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 2 inches. (Give the answer in terms of π and r.) V(r) = 4/3 pi r^3

The amount of the air needed is exactly $$V(r+2)-V(r)$$ $$(4/3)\pi(r+2)^3-(4/3)\pi r^3=(4/3)\pi((r+2)^3-r^3)$$ $$=(4/3)\pi(6r^2+12r+8)$$