All you need is a function that gives you the new air you need to put in. You need the volume of a sphere of radius r+1 that is not in a sphere of radius r, i.e. the difference between them.
Course & Textbook Calculus Essential Calculus Early Transcendentals - Newest edition Chapter 1.1 Problem 18
A spherical balloon with radius r inches has volume V(r) = 4/3?(r^3). 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+1 inches.
I gotta be dumb but I'm not certain how to carry through the cube cause I don't have the solution.