a. Find the radius and height ofa cylindrical soda can with a volume of412 cm3 that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a volume of412 cine, a radius of3.1 crn' 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 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? a. Write a function for the surface area of the soda can, 8, in terms ofthe radius, r, 824 s : 7 + 2 r (Type an expression ) The interval of interest ofthe objective function is El (Simplify your answer, Type your answer in interval notation ) The radius is approximatelycm. (Round to two decimal places as needed.) The height is approximatelycm, (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? _No _ Yes