## Calculus: Early Transcendentals 8th Edition

A(r)=4$\pi$$r^{2}+4\pir+\frac{4}{3}$$\pi$
Let the amount of air required as a function of the original radius of the balloon be A(r). A(r) = V(r+1)-V(r) = $\frac{4}{3}$$\pi$$(r+1)^{3}$-$\frac{4}{3}$$\pi$$r^{3}$ = $\frac{4}{3}$$\pi[(r+1)^{3}-r^{3}] = \frac{4}{3}$$\pi$[$r^{3}$+3$r^{2}$+3r+1-$r^{3}$] = $\frac{4}{3}$$\pi[3r^{2}+3r+1] = 4\pi$$r^{2}$+4$\pi$r+$\frac{4}{3}$$\pi$