The Cup Design Module:
AutoCAD and Geometry

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Example Plan

An Example of a cup design
by George Reese 3/5/98

Ok, here is my effort at the optimal paper or plastic cup. Mine would probably be plastic, since it would be tough to get paper into the arc that I would like.

My criteria for the optimal cup were

  1. To meet the requirements of the assignment (16 oz., must stand up, as little material as possible, etc.)
  2. To be easy to grip. I want a cup that is easy to grab without looking.
  3. I want the cup to be very stable, again, in case I bump it when I'm trying to pick it up while my mind is on writing HTML modules.

So, I want a cup with a wide bottom, tapering in the middle (for gripping) and widening at the mouth so that it's easy to drink from.

To design my cup I used the two-dimensional tool Geometer's SketchpadÆ.

Here are the steps to my design.

First I made a sketch on the computer. This let me play around with the design a bit. I used a simple painting tool called MSpaintÆ .

This was the drawing that I made. It's a
frustum at the bottom, and the top is simply
the arc of a circle rotated 360 degrees around
a point outside the circle on the center axis
of the cup.

In the Sketchpad files, I look at the base of
the cup and the top of the cup separately.

Next, I divided my design into two sections.

The bottom part of the cup is a frustum.
The top is made of the arc
of a circle rotated around an
exterior point.

Then, I wanted to find out what the specifications for my design would be. I used Geometer's Sketchpad and created a file that would allow me to play with the dimensions. One thing I had to be sure of was that it would hold at least 16 ounces. So I went to Ed's Metric Conversion Chart to figure out how many cubic centimeters were in an ounce. This was a little tricky, since Ed's chart only gave me the relationship between liters and ounces. But I figured it out. Turns out there are just a little over 473 cubic centimeters in 16 ounces.

NOTE (1/10/00): Ed's Metric Conversion chart is no longer available, but a new ad hoc converter has been made by Jim Dildine. It's better suited to this project.
Check it out at

Here is the Sketchpad file that I created to determine the dimensions of my cup. It is also saved as a Java Sketchpad file so that you can view it right in your browser if you have Netscape version 3.0 or higher.

I thought of three formulas for the volume of the base piece:

Which one is correct?
I chose the second one.

Send me email and I'll tell you why.


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