Grocery Store Cans How "volume optimized" are the cans that we buy from the grocery store? Suppose you could melt the metal down and use it to make a new can. What is the largest volume you could make with the same amount of metal/aluminum? To simplify the problem, assume that all cans have the same thickness. We will use only surface area to calculate the amount of metal used for the can. Find 3 different sized cans. You can use soda cans, soup cans, tuna fish cans, etc. and calculate the amount of metal used to make each can. Then, for each can, calculate the maximum amount of volume the metal could hold in theory. Determine how "volume optimized" each can is by finding the following: actual volume of can maximum volume of can Give the final answer as a percent. Your final report should include: Pictures of each of the three cans you used. The height, radius, surface area, and volume of each can A clear explanation of how you algebraically calculated the maximum possible volume for each can. The percentage of how "volume optimized" each can is. A graph (for each can) showing the volume versus the can's radius. Mark the point on the graphi which represents the maximum possible volume and the point on your graph which represents your actual can.