Last week, people blew lots of balloons for decorating the celebration arena. Suppose air was being pumped into each balloon at a rate of 4 cm³/sec. What is the rate at which the radius of the balloon is increasing when the radius of the balloon is 6 cm.

We know the volume of a sphere is V=4/3πr³. Then we do the derivative which is dv/dt=(4πr²)(dr/dt). From the question, we get r=8, dv/dt=3. Plug these numbers into the equation, we get 4=(4π6²)(dr/dt). Therefore, dr/dt=0.00884 cm/sec.