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A soda can manufacturer wants to minimize the cost of the aluminum used to make their can. The can has to hold a volume V of soda. Assuming that the thickness of the o _ can is the same everywhere, the amount of aluminum used to make the can will be proportional to its surface area. That is. suppose the height of the can is h and the radius of the can is r, as shown in the gure on the right. A soda can is a circular cylinder with radius r and height h. The curved surface area is 23trh and the area of each end cap is 1:3. Then the manufacturer wants to minimize S = 27crh + 2m2 subject J to the constraint that xrzh = V. Here we have used the formulas for the total surface - area and volume of a cylinder. Complete parts (a) through (d). (a) A real soda can has volume V = 256 cm3. By substituting for h in the given equation, write S as a function of r only. Sir) = E (Type an expression.)