There are many ways to visualize that the volume of a pyramid is ⅓ of the volume of its corresponding prism. While my favorite class demonstration is to use a geometric volume set like this one to pour 3 pyramids of water into the corresponding prism while making my class guess how many times I have to pour.

Another way to visualize the ⅓ volume principle is to decompose a rectangular prism into pyramids. These are the ways I have seen over the years:

• Have an asymmetric square pyramid with the top of the pyramid over one of the corners. 3 copies of this pyramid make a cube.
• Have a symmetric square pyramid with ½ of the height of the cube. 6 of the pyramids connect so the tips of the pyramids are in the center of the cube. Because of the ½ height, you need to double the height getting the ⅓ fraction.

Each of these methods has a corresponding model.

I used round magnets from DIYMAG that were marketed at 10mm x 2mm (10mm diameter and 2mm height), but when I measured using my calipers, I found that the diameter was 10mm and the height was really 1.77mm. I added a clearance gap of .25mm to each magnet hole and they fit snugly when I printed on my Prusa Mini in PLA + from Elegoo.

Gluing the magnets:

I don't use hot glue because I read that (1) it isn't as strong as super glue and (2) heat can decrease or ruin the magnet's magnetism. I use Gorilla Super Glue Gel. It sets in under a minute. Wear disposable gloves if you don't want super glue on your fingers. For the amount of glue I just used trial and error. I would describe the amount as a half of a pea if that helps.

A note about the magnet polarity: For the slant pyramid having 2 different polarities in each piece should work. For the 6 pyramid models I put magnets in the same polarity on adjacent faces (corners were the same polarity). I still messed one up because I wasn't paying enough attention and had to reprint it (the glue sets REALLY fast and is REALLY strong). If I had to redo this project again I would make 1 piece and let it set. Then I would put the magnets on the existing piece, put glue on the 3D print, squish the 3D print onto the exposed magnet, slide the pieces apart, and then wipe off any extra super glue. This will make it impossible to put the magnets in wrong.

Printing and Materials:

3 "Pyramid Volume slant.stl" & 6 magnets

6 “Pyramid Volume half height.stl” & 24 magnets 

Gorilla Super Glue Gel