End of the Year Calculus Project

Whew! That's done. We celebrated Cinco de Mayo by having an AP Calculus AB exam. Aye yai yai yai! After the exam it's a mix of attendance and other issues for students, and every year I have done slightly different things. This year, I wanted to revisit "projects". I had an awful time the last time I did this. Granted, I let the kids have free reign with their time, and shockingly, some chose to waste it (who would have thought), and this resulted in the most memorable string of e-mails from a parent who claimed it was all my fault a student got a bad grade and the kid would now not get into his choice school and his life was ruined and what kind of monster was I? So you can maybe see why I hesitate to do a project. 

Flash forward to this year. I wanted to do a project (because I never learn), but I wanted a Volumes of Revolution project. My specs:
* Must be cheap.
* Must be done only in class with no homework.
* Must involve creativity.
* Must involve calculus.
* Must be fast.
* Must be original.
* Must pull some other math topics from bygone years.
* Must use technology.

And voila! Here are the benefits (I hope) of this project:
* Involves scratch paper and tape/scissors and MAYBE pretty paper.
* I believe it can be done in 2 or 3 block schedule classes.
* Students create their own functions.
* They have to calculate the volume of revolution.
* They have to know how to calculate the radius if given the circumference.
* Regression website! Desmos!

 So I give you THIS. Let the fun begin.