# Blog Archives

## Calculus Final Project Spotlight: 3D Solid Modeling

**The next few posts are going to be spotlights of final projects that students did that I thought were cool or interesting and then a few reflections on doing final projects in general. I could picture doing a lot of my student’s projects as a whole class!**

If I had one more week in my non-AP Calculus class, we would study volumes of revolution. That’s probably the biggest weakness of my course right now, and I am trying to figure out a way to include that next year. A junior who is in my regular class and is taking AP next year was a bit lost when coming up with an idea, so he asked me for a topic that we do in AP but did not do in our class so he could be a bit prepared. I suggested volumes of revolution and after a lot more nudging and guidance and idea planting than I did for other students, we decided that a good project for him would be to recreate an interactive 3D model of a solid of revolution using GeoGebra and Winplot. (actually it works with solids of known cross section too).

### Here’s how it works…

1. Upload a picture into GeoGebra (he chose a huge vase from the art room). Fit functions to the edges of the object on the part that will be revolved.

2. Recreate the same exact functions in Winplot (which has much better 3D capabilities than GeoGebra does).

3. Use Winplot’s revolving capabilities to revolve the surface around an axis (any axis!). And then, voila, you have a 3D model of your object that you can use the arrows on the keyboard to rotate in any direction. It actually ends up being really impressive – my student told me that he left the model up on his computer and every time he would turn it on he would rotate his vase a bit.

After I saw the success of this project, I suggested the same one to a few students in my AP class (who were required to do a much more low key, shorter version of a final project because of time restraints). They decided to recreate a bunch of sports equipment using the program, which I thought was a really cool idea! Their rotate-able objects:

NEXT YEAR: I made an instruction sheet for those AP kids because they had less time, but I’m glad I did because this was a really cool project and is something that I can see myself doing with a whole class next year. Here it is below. If you haven’t tried making any 3D models (not necessarily real objects) with Winplot, definitely try it out – it’s super cool!