[Note: 10:30 am on Oct 7th, 2017 – had a hard stop time to get this out the door, so it is published without editing. Will (or might!) edit a bit later]
About two years I found an amazing design by Steve Portz on Thingiverse:
“Archimedes Proof” by Steve Portz on Thingiverse
We did a really fun project using the print back then:
The volume of a sphere via Archimedes
Today we revisited the idea. We began by talking generally about the volume of a cylinder:
The next part of the project was heading down the path to finding the volume of a cone. I thought the right idea would be to talk first about the volume of a pyramid, so I introduced pyramid volume idea through snap cubes.
Also, I knew something was going a little sideways with this one when we were talking this morning, but seeing the video now I see where it was off. The main idea here is the factor of 3 in the division. Ignore the height h that I’m talking about.
Next we looked at some pyramid shapes that we’ve played with in the past. The idea here was to show how three (or 6) pyramids can make a cube. This part was went much better than the prior one 🙂
The ideas here led us to guess at the volume formula for a cone.
Now that we’d talked about the volume formulas for a cone and a cylinder, we could use the 3d print to guess at the volume formala for the sphere.
With all of that prep work behind us, we took a shot at pouring water through the print. It worked nearly perfectly 🙂
I am really happy that Steve Portz designed this amazing 3d print. It makes exploring some elementary ideas in 3d geometry really fun!
Mike's Math Page 