Volume of Revolution Project

This past year I tried something new with my calculus students for the "volumes project" in the oh-my-goodness-what-to-do-after-the-exam phase of the year (closely linked to the eek-I-hate-giving-class-time-to-do-projects-and-can-they-waste-any-more-time phase of teaching calculus).

I did the project with the kids to see what was involved, and I told them it was the first time I'd done this, so we'd learn the pitfalls and tips and such together. I also was vague on how they should display the projects at the end. I said, "wow me" and "whatever you do, have a good reason for it" and "think of the best way to display it to use as a learning tool".

The general idea was that we'd all have the same starting 2-dimensional region (y = 4 - xx), and we'd each revolve it around a different axis of revolution, and thus each have different solids at the end.

She wowed me with her final presentation:
This is mine (I now realize I took the picture upside down). Hmmm, spaghetti/math-tool ... probably not too long lasting:


Before she started, she kept saying, "I want to make it into Saturn", so I guess she continued with her space theme:

He was so funny, "tell me what to do. tell me what to do." Me, "no. no. NO.". He finally came up with it himself: