Problem statement
What exactly is the ideal size of a soda can? Throughout this problem you are to find the volume and surface area of a standard sized Coca Cola can and create additional cans using our own size specifications, but still keeping the volume of 365cm^2 a constant. By the end of this POW we should have the specs for the "dream" Coca Cola can and the savings the Coca Cola company would have if they manufactured this can.
Process
One of the very first steps I took was finding the volume and surface area of a standard 12 oz Coca Cola can. After I had found my volume of 365cm^2, which had to be kept a constant, I moved on to creating the specs of my own cans. While trying to keep my volume constant I derived the specs from π r^2h=365 by plugging in a variable for r or h.
Solution
Dream can:
Total savings if manufactured:
- Radius: 4cm
- Height: 7.2 cm
Total savings if manufactured:
- $37 billion
Reflection
This POW is a great example of a "real world problem", it not only implemented what we are going over in math class, but had many real world elements. In corporations as big and as successful as Coca Cola there are people who are payed to do what we did in POW. These types of "real world" problems gives a student of what it is like in a working environment, collaborations, solving smaller problems, and visualizing are the habits of a mathematician I used in this POW and are only a small sliver of the habits of a mathematician I will use in a working environment.