6. 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 Python, solve for the size of a can that would minimize the 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?