Problem Statement
I think that it is best for coke to maintain their current can size. If they were to switch to a different can size they would have to completely redo all of their factories in which anything could go wrong and it would be expensive, and there would also be a shortage of Coca-Cola due to some factories having to be shut down. Once their is a lower production rate, there is a higher demand than there is a supply, and by the time that happens, Coca-Cola will have to raise their prices on each soda in order to maintain their profits. All of this in order to save a mediocre amount per can. In the end, I do not think it is worth switching soda can sizes.
Process Description
In order to come up with the conclusion that I found, we first had to see just how much Coca-Cola could save while still being able to hold the same amount of liquid in each can. First, we had to plug in a height and a radius that would make up the same volume a normal Coke can. We used the formula π(r2)(h) to find the volume of the cans that we made up. After finding measurements that fit the criteria, we had to solve for the surface area of the cans by using the formula 2π(r2)+2π(r)(h). Then, we gathered data from other classmates and plotted the points on a line graph. There was a small pattern found in the sense that the points made a parabola of sorts. After that, we had to discover the radius of the least expensive can and find the height.
Solution
The cheapest price for a can would be $0.02, only $0.02 less than the original cost, therefore not making it not worth it to change the can size.
Reflection
I think that I learned a lot about volume and surface area from the Canalyisis problem. I also think that that I used a lot of Habits of Heart and Mind during this P.O.W, but, the two that I thought I used the most would have to be taking apart and putting back together and staying organized. I applied taking apart and putting by together by having to solve multiple equations in one and using one equation for the other. I had to apply staying organized in order to successfully take apart and put back together. I think that I deserve an A for this P.O.W. because I cooperated with people around my table in order to find the correct solution for certain problems.