Prisms and Pyramids

An interesting relationship exists between the volume of a cylinder and the volume of a cone that has the same height and same base area, namely, the volume of the cylinder is three times the volume of the corresponding cone. That same relationship exists between the volume of a prism and the volume of its corresponding pyramid.

These objects I've uploaded can be used with students to demonstrate this relationship. For example, if you fill the cone with water, sand, or rice, and then empty the contents of the cone into the corresponding cylinder, you'll find that you will have to repeat this process three times to fill the cylinder.

I am a teacher of blind and visually impaired high school students. I composed these objects in OpenSCAD to be used with my students to illustrate the concept of the relationship between the volumes of the pointy objects and their corresponding non-pointy objects. However, these objects can be used with any student, visually impaired or not, to illustrate this important relationship.

Regarding the spherical knob I placed at the top of the pointy objects, I put that there to avoid the cooling/deformation issues that occur with most printers when printing pointy objects. Also, it looks cool!

I also included the .scad files of these objects for anyone who wants to tweak the objects for their own purposes. It occurs to me that this may help other teachers to play with OpenSCAD, and learn to use it for the benefit of their students.

I will upload pictures of my prints of these objects soon.

Have fun!