Please use 3 cans and calculate this for me.

Question: Are the cans in the store "volume optimized? Think about calculus through a shopping trip and investigate its hidden use behind everyday objects, like cans. Each can in the store is made of a certain amount of metal. Think like you will melt that metal down and reforge it into a different sized cylinder which holds even more volume. In other words, does that metal (used for the actual can) enclose the most volume it could? Find 3 different sized cylindrical cans (e.g., soda can, soup cans, red bull cans, Arizona iced tea cans, tuna fish cans, etc.), calculate the actual volume and the amount of material used to make each can. The surface area will suffice - we aren't going to take into account the thickness of the cans. For each can, you need to calculate (by solving an optimization problem) what is the maximum amount of volume the metal used for the can (expressed as area) could hold in theory. Then you're going to calculate how volume optimized each can is, by calculating the ratio: (The actual volume of can) = (Best possible volume of can) Which, as a percent, represents how close the actual volume of the can is to the highest volume" possible (for the given surface area of the metal). Your final product should include: A. more interesting (clever) tittle that the question above is appreciated. Photographs of each of your cans, The height, radius, surface area, and volume of each can labeled, The maximum possible volume for your cans with a clear explanation of how you algebraically calculated it Show how "volume optimized each can is Make a graph of the can's volume versus the can's radius, and mark the point on the graph with the maximum possible volume, and mark the point on the graph which represents your actual can Question: Are the cans in the store "volume optimized? Think about calculus through a shopping trip and investigate its hidden use behind everyday objects, like cans. Each can in the store is made of a certain amount of metal. Think like you will melt that metal down and reforge it into a different sized cylinder which holds even more volume. In other words, does that metal (used for the actual can) enclose the most volume it could? Find 3 different sized cylindrical cans (e.g., soda can, soup cans, red bull cans, Arizona iced tea cans, tuna fish cans, etc.), calculate the actual volume and the amount of material used to make each can. The surface area will suffice - we aren't going to take into account the thickness of the cans. For each can, you need to calculate (by solving an optimization problem) what is the maximum amount of volume the metal used for the can (expressed as area) could hold in theory. Then you're going to calculate how volume optimized each can is, by calculating the ratio: (The actual volume of can) = (Best possible volume of can) Which, as a percent, represents how close the actual volume of the can is to the highest volume" possible (for the given surface area of the metal). Your final product should include: A. more interesting (clever) tittle that the question above is appreciated. Photographs of each of your cans, The height, radius, surface area, and volume of each can labeled, The maximum possible volume for your cans with a clear explanation of how you algebraically calculated it Show how "volume optimized each can is Make a graph of the can's volume versus the can's radius, and mark the point on the graph with the maximum possible volume, and mark the point on the graph which represents your actual can