After looking over the entire structure of the problem we answered in class which was to find the dimensions of the aluminum can, 12 oz in volume, that would minimize the surface area (amount of aluminum) used. Make sure you understand how we managed to verify that our values after using calculus were in fact the ones that would minimize the surface area. Then, consider the dimensions of the can we have found to be most economical and consider it containing soda. Next answer the following:
An actual can of Coca Cola is not a perfect cylindrical container and its dimensions do not correspond to those that minimize the material cost of manufacturing the can found above. The radius of an actual can is 3.413125 centimeters and height is 12.22375 centimeters. Why do you think that an actual Coca Cola can does not have the dimensions found by the optimization problem above?
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