Last month GeoGebra, the free multi-platform graphing and math program, came out with version 5, which includes three-dimensional graphing. As a geometry and calculus teacher, I was ecstatic and immediately set out to do whatever I could do. Here are some of the things I made for my calculus classes:
This is a standard maximize the volume of the cone question. Here's the GeoGebra file.
There's lots of fun stuff to do with the volumes by known cross-section:
The slices are semi-circles, and the slicing plane makes that clear. Here's the GeoGebra file.
Here is a solid where the cross-sections are equilateral triangles:
Here's the GeoGebra file, and a video on how I made a similar construction.
One can also set up rotational solids pretty easily:
Here's the GeoGebra file, and a video on how to construct it.
And here is a more complicated region:
Here's the GeoGebra file.
And my previous post had a nice GeoGebra demo on conics (made by a colleague, not me).