Question

Air is being pumped into a spherical balloon at a constant rate of 15 ft^3 per min. At what rate is the surface area of the balloon increasing at the moment when the radius is 2 ft?

Answer 1

\[A=4\pi r^2\]\[V={4\over3}\pi r^3\]\[{dV \over dt}=4\pi r^2{dr \over dt}=15\]solve this for dr/dt and plug that value into \[{dA \over dt}|_{r=2}\]