A spherical ballon is inflated with helium of a rate 90pi ft^3/min. how fast is the balloons radius increasing when the radius is 3ft?

Answer 1

given: dV/dt = 90π f³/min and balloon is a sphere. V=4/3πr³ so dV/dt =4πr²dr/dt (chain rule). Use algebra to re-arrange to find dr/dt =dV/dt/(4πr²). Substitute 3 for r and 90π for dV/dt to yield dr/dt = 2.5 f/min.