Optimal soda can a. Classical problem Find the radius and height of a cylindrical soda can with a volume of 354 cm3 that minimize the surface area. b. Real problem Compare your answer in part (a) to a real soda can, which has a volume of 354 cm3, a radius of 3.1 cm, and a height of 12.0 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 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?

Solution 39E Step 1: (a) Consider a cylindrical soda can with the volume of cm . Let the radius of the cylinder be and eight be . Consider that the volume of the cylinder with radius and height is given by the following formula V = r h2 …(1) So, in this case volume is, V = r h = 354 h = r2 Now, the total surface area of the cylinder with radiusr and heighth is given by the following formula A = 2r +2rh ….(2)