**Spaghetti
holes **

I want to make one of those measuring tools for spaghetti. ItÕs a board with holes of various sizes in it. ThereÕs a hole through which you stick enough spaghetti to feed 2 people, another hole for 3 servings, another for 4. I know that the hole for 2 servings has a diamter of 1 inch. How large should the other holes be?

**Approaches**

guess and check

find area for 1 person, then set up and solve equaations for other numbers of people

area ratios: diameter of hole for 3 servings is the square root of 3/2 times the diameter of the hole for 2 people.

see pattern in data for 1, 2, 3, 4 servings, note constant second differences, find quadratic function for prediction

Does pattern hold for 0 servings?

**Your
experience**

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

*Last updated 30 November, 2004*