Assessment

Evaluation & Assessment
Verifying the Plan's Effectiveness

Students will be asked to complete a worksheet similar to the following as they conduct this project. The worksheet includes several open-ended questions that will help identify individual students' understanding as opposed to group calculations.

Klutzy-Cola, a national soda bottling company has fallen on hard times. The soft drink giant is losing money and the board of directors have called in a mathematician for a little advice.

Since price of aluminum is skyrocketing. The company wants to see if there is a cheaper way to design their soda cans. The company asks you to come up with the cheapest soda can available. Here's what you know:

The can must hold 12 fluid ounces of soda.
Twelve fluid ounces is equivalent to 355 Mililiters.
355 mililiters is 355 cm^3.
The cheapest soda can will have the smallest surface area.
The surface area of a cylinder is SA=(2*Pi*r^2)+h*2*Pi*r.
The volume of a cylinder is V=(Pi*r^2)*h.

The current Klutzy-Cola can measures 10 cm high by 7 cm wide.

Please write the radius of the current can (include units):_________________

Please calculate and write the surface area (include units):_________________

Please calculate and write the volume of the current can:__________________

Can you think of some reasons why the volume of the can is different from the volume of the soda? Would you list any you can think of, please?

For this project, we will design a can with a volume of 355 cm^3.

Would you please use the following formulas to complete the following table? Pick any three values of r you like.

r Pick any #	h h=56.53/r^2	SA SA=2Pir(r+h)

Can you start to guess what the best value of r might be? Let's use the calculators since these calculations are pretty long & tedious.

Complete this table for more values. Try to narrow in on what value of r will give you the smallest surface area.

r Pick a #	h h=56.53/r^2	SA SA=2Pir(r+h)

Now do you have a good guess at what values of r & h will give you the best soda can? Let's use the calculators to find out exactly.

Press the "Y=" key and enter the following equation and plot it:

Y=2*Pi*x*(x+(56.53/r^2))

Sketch your graph below.

Y is the surface area of your soda can and x is the radius. We want the x value at the lowest point of the graph. Use the calculator's trace and minimum functions to find this value.

Please complete this table with the data on your most efficient soda can.

SA=

Do you believe this really is the most efficient soda can design?

Can you think of reasons why soda companies don't make containers with your measurements?

What are some other considerations soda companies think about when designing soda containers?