Math 63 Activity Section 2.2: Coffee Cup Design Name:
This assignment is worth 2 quizzes. You must show your work. No work, no credit.
Materials: Paper, Rulers, Protractors, Compasses, Tape
Directions: Design and build a coffee cup that will hold 12 ounces. Note that there are 29.574 cm3 in 1 ounce.
1) Change 12 ounces into cm3
2) You choose R = ______
and r = ______
3) Using the volume formula, substitute in the known values and calculate the height (h) for your cup.
Volume formula:
Before you draw your coffee cup design, there are a few more calculations you will need. The shape on the right must be drawn to precise dimensions using the following formulas. You will need to use the values that you found for R, r and h to determine the values for x, y and A..
1. Use the formula to find a value for ”y” to the nearest tenth of a centimeter:
2. Use the proportion to find a value for ”x” to the nearest tenth of a centimeter:
3. Use the proportion to find a value for “A” rounded to the nearest tenth of a degree:
Note: You will need a bottom on your cup. It will be a circle of radius r.
The diagram you draw may not fit on a single sheet of paper. The sides of the angle may be quite long. You will probably need to tape a couple of pieces of paper together in order to draw the actual lengths.
You will need a protractor to measure angle A. When you are ready to draw the arcs, a normal size compass will probably not do the trick. Try pinning a string at the bottom tip, tie a string at the other end and sweep an arc. The length of the string will be x + y.
After drawing the diagram, cut it out and then trace it on to a piece of cardstock. Connect the edges with tape then secure the bottom of the cup with tape. We will be measuring how much it will hold by filling it with rice.
Your design will be tested to see how accurately it holds exactly 12 oz of rice.
Enter your findings (this will be done in class):
My cup held more/less (circle one) than 12 oz. My cup help approximately ______oz.