Solve the following

Part 1 of 7 Points: 0 of 1 a. Find the radius and height of a cylindrical soda can with a volume of 434 cm" that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a volume of 434 cm", a radius of 3.1 cm, and a height of 14.7 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 find 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, S, in terms of the radius, r