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Another Classic Problem: A can is made in the shape of a right circular cylinder and is to hold one pint. (For dry goods, one pint is equal to 33.6 cubic inches.)
(a) Find an expression for the volume V of the can in terms of the height h and the base radius r.
(b) Find an expression for the surface area S of the can in terms of the height h and the base radius r. (Hint: The top and bottom of the can are circles of radius r and the side of the can is really just a rectangle that has been bent into a cylinder.)
(c) Using the fact that V = 33.6, write S as a function of r and state its applied domain.
(d) Use your graphing calculator to find the dimensions of the can which has minimal surface area.
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