in. Find the radius and height of a cylindrical soda can with a volume of 412 Cm3 that minimize the surface area b. Compare your answer in part (a) to a real soda can, which has a volume of412 cma, a radius 013 1 cm' and a height of 14 0 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 ofthe top and bottom are now twice Their values in parl (a)]. Are these dimensions closer to the dimensions of a real soda can? a. Write a function for the surface area of the soda can, 5, in terms of the radius, r 5: (Type an expression ) The interval of interest of the objective fundion 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] I). The new radius is approximately _cm (Round to two decimal places as needed) The new height is apprommately_' cm. (Round to two decrmai places as needed.) Are these dimensions closer to the dimensions of a real soda can? No _ Yes