B = Area of the Base

h = Height of the figure

Volume Formula:

Pyramid: 1/3Bh

Cones: 1/3Bh

:

So what this is telling me

A pyramid fits perfectly inside a prism and takes up 1/3 of the volume.

A cone fits perfectly inside a cylinder, and takes up 1/3 of the volume.

My Question:

How do I know this? How was this figured out?

I am trying to find a way to explain this to my 7th grade students without forcing them to take my word that this is true. I want them to KNOW this is true.

My first instinct was to create a model to represent it but that is easier said than done.

The only thing I have been able to tell them so far is that it is just like area of a triangle, but with 3d shapes. However, unlike triangles, I have been unable to show them.