a. Find the radius and height of a cylindrical soda can with a volume of 398 cm3 that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a volume of 398 cms, a radius of 3.1 cm, and a height of 13.5 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to nd the radius and height that minimizes the surface area of a real can (the surface areas of the top and bottom are now twice their values in part (a)). Are these dimensions closer to the dimensions of a real soda can? E) a. Write a function for the surface area of the soda can, S, in terms of the radius, r. s = (Type an expression.) The interval of interest of the objective function is . (Simplify your answer. Type your answer in interval notation.) The radius is approximately cm. (Round to two decimal places as needed.) The height is approximately cm. (Round to two decimal places as needed.) b. The new radius is approximately cm. (Round to two decimal places as needed.) The new height is approximately cm. (Round to two decimal places as needed.) Are these dimensions closer to the dimensions of a real soda can? Yes No