6. (10 pts) The typical soda can is 2.5 inches in diameter and 4.5 inches high....

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6. (10 pts) The typical soda can is 2.5 inches in diameter and 4.5 inches high. You would think that the cans would be designed such that the total surface area is minimized, thus minimizing total material costs. However, the size of a soda can (2.5 inches in diameter and 4.5 inches high) is NOT the optimum size that minimizes total surface area. a. (9 pts) Using Matlab, solve for the size of a can that would minimum total surface area that has the same volume as the typical soda can (2.5 inches in diameter and 4.5 inches high). b. (1 pt) Based upon your result from part a, why do you think soda cans are designed the way that they are? In other words, why do you think a soda can is 2.5 inches in diameter and 4.5 inches high and NOT the dimensions you find in part a? 6. (10 pts) The typical soda can is 2.5 inches in diameter and 4.5 inches high. You would think that the cans would be designed such that the total surface area is minimized, thus minimizing total material costs. However, the size of a soda can (2.5 inches in diameter and 4.5 inches high) is NOT the optimum size that minimizes total surface area. a. (9 pts) Using Matlab, solve for the size of a can that would minimum total surface area that has the same volume as the typical soda can (2.5 inches in diameter and 4.5 inches high). b. (1 pt) Based upon your result from part a, why do you think soda cans are designed the way that they are? In other words, why do you think a soda can is 2.5 inches in diameter and 4.5 inches high and NOT the dimensions you find in part a?