Need Help on a Project, very new to Blender

For my geometry class, we have to make an animation or some sort showing a visual proof for the surface area of one of a few prisms, I am choosing a cone. I already know the math behind it, I just needed some help with the animation. Some people are making flip books some people are doing stop motion with a camera, but I thought this would be a great opportunity to get into 3D design. I downloaded blender the other night, and so far I have just been messing around in it, trying to get a feel for everything, but I am stumped on how I am supposed to animate something like this http://www.youtube.com/watch?v=ZXf-IokKSLU.

Any help would be appreciated

p.s. I wasn’t sure exactly where to post this, so if this is the wrong place feel free to let me know, and I can move it.

How about separate all the parts of the cone into objects and animate the parts one at a time.
I do not understand how the math works cause the edge is round then squared on the parallelogram.