GeoGebra 5 -- into three dimensions

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).