Pyramids and Cones

Last week in math class we did an activity called "Pyramids and Cones". It helped to show us the relationship between the volume of a pyramid and prism with the same base and height and also the volume of a cone and cylinder with the same base and height.

First, we started out with nets for the prism, pyramid, cone, and cylinder. We cut them out, folded, and taped them. I have to admit, I did have a little trouble with this part. By the time I completed the pyramid, my partner had practically finished all the rest. After assembling our shapes we observed that our pyramid and prism shared the same base and height. Our cone and cylinder shared the same base and height as well. We were then asked to estimate how many pyramids full of rice would it take to fill the prism. My estimation was that it would take 2 pyramids of rice to fill up the prism. We then filled up our pyramid with rice and began to pour it into the prism. Note that our shapes had no cover over the base so that we could fill them. To my surprise, it actually took 3 pyramids to fill up the prism. We then went on to estimate that it would take 3 cones to fill up the cylinder. After filling up the cylinder we verified our estimation. For some reason I could imagine it taking 3 cones to fill up a cylinder, but I was surprised that it took 3 pyramids to fill the prism. Because we were able to measure the volumes ourselves, this activity was very helpful to me. If I had just been told that a prism is 3 times the volume of a pyramid, I could have easily forgotten this. However, this activity provided me with a visual memory that I will be much more likely to remember.

Here is a video of a similar demonstration being done.