1. Student Sample: Soda Can Designs
Class: EDSC304
Instructor: Professor Crocco
Student: Thanh Diep

2. Student Sample: Project—Explaining Soda Can Designs
In this student sample project, student A demonstrates his/her knowledge in solving optimization problems, that he/she has learned in the class, to explain the soda can designs.
Format: the project format is of a story-telling– a conversation between student A and student B.
The project purpose is to answer the curriculum-framing question: “How can calculus be applied in the real world.”

3. What is the size of a soda can?
Student A asks student B:
Do you know what the size of a soda can is?
Student B:
Yes, its diameter is 6cm and its height is 12cm.

4. Why the height is twice the diameter?
Student A:
Then do you know why the height of the soda can is twice the diameter of the can?
Student B:
I don’t know why but I think it is for reducing the cost of making the cans.
When the height is twice the diameter, we can make the can with smallest amount of material because that is when the total surface area of the can is smallest.
Student B: Really! Can you prove it?
Student A: Yes, let me show you the proof by doing the math.

5. Doing The Math

6. My 21st Century Skill
Student A: I also know how to plot a function using computer-aided software such as Matlab. You can see from the plot below, the surface area of a soda can has a smallest value when the height of the can is equal to the diameter of the can.

7. Mini-Soda Cans Have Smallest Surface Area
Student B: So mini-soda-can dimensions have smallest surface area, but why the diameter is 6 cm and the height is twice?
Student A: The diameter is chosen to be 6 cm because it fits in most people’s hands. And if we make only mini-soda cans of the size 6 cm by 6 cm, they are too small for the average person.
Student A continues: so we come up with an innovative solution. We pack two mini-soda cans into one regular-size can and this method helps reduce the surface area further as shown on the next page.

8. Regular-Size Soda Cans Reduce Surface Area Further
Student A: That is why a soda can is the size of 6 cm by 12 cm for which the height is twice the diameter.

9. Other Brands are the Same Size
Student B:
It’s an amazing story. Now I happen to realize that all the soda cans have the same size; and the height is twice the diameter!

10. Final Thoughts and Conclusions
Student B: I can’t believe that even in a soda can, calculus has been applied.
Student A: So what is your final thought?
Student B: I’ll take calculus next semester!
Student A: Here are some online free calculus lectures.
Conclusions:
In this sample project, student A has:
made connection between his/her unit knowledge in finding minimum values of a function with the real world soda can designs.
demonstrated his/her 21st century skill by using computer-aided software to plot functions.
demonstrated his/her knowledge of the unit by using first and second derivative tests to find minimum values of a function when explaining the soda can design.