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The Disc Problem (doc  pdf)
A can of soup, a coin, and a piece of spaghetti are all cylinders even though they look very different. One might say the coin is more “disclike” than the spaghetti.
1. Given the variety of cylinders you have: Devise a definition of discness that allows you to say which object is the most disclike and which is the least.
2. Write a formula (or algorithm or algebraic sentence) which expresses your measure of discness. You may introduce any labels and definitions you like and use all the mathematical language you care to.
3. Make any measurements you need, and calculate a numerical value of discness for each of the six items.
4. Discuss whether these numbers seem reasonable in light of your notion of discness.
5. How would you change your answers to these questions if you were asked to write a formula for cylinderness rather than discness?

