Question

A spherical balloon with radius r inches has volume V(r) = 4 /3 πr3. 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 + 4 inches. (Express your answer in terms of π and r.)

Answer 1

\[\frac{4}{3} \pi (r+4)^3-\frac{4 \pi r^3}{3}=\frac{16}{3} \pi \left(3 r^2+12 r+16\right) \]