Soda cans usually hold 355 cc (12 fluid ounces, that is) of liquid. It seems likely that the manufacturers of these cans choose the dimensions so that the material required to enclose those 355 cc is as small as possible. Let us find out.

(a) Give an example of a right circular cylinder, choosing its radius and height to make the volume 355, then calculate the total surface area of your cylinder, in square cm. 

(b) Express the height of such a cylinder as a function of its radius r. 

(c) Find the value of r that gives a cylinder of volume 355 the smallest total surface area that it can have. Calculate the resulting height, and compare these two dimensions with the actual dimensions of a soda can.