A cylindrical can must contain a fixed volume of 600. In this problem you will find the radius of the can which will minimize its surface area. The applet above shows a plot of the surface area function. Use the slider to visualize how the surface area changes for different values for the radius, and use the corresponding graph to estimate the optimal radius. Then use calculus to find an exact answer.

First, determine a function which gives the surface area of the can in terms of its radius (this is the function plotted above):

Now use calculus to find the exact radius which minimizes this surface area:

What is the exact height of the can of minimal surface area?

You can earn partial credit on this problem.