Making pyramids

In Grade 9 today we looked at how pyramids are related to prisms of the same base and height.

We filled the pyramids with water, and could dump them 3 times into the prism to fill them up. The volume of the pyramid is one third the volume of the prism with the same base and height.

We then worked on building pyramids with a volume of 300cm^3.

Some of us made an error that we can learn from. For some of us the pyramids ended up being shorter than we planned. We measured the pyramid height as the slant height of the pyramid (the height of the triangular face).

We can see that there is a right angle triangle hidden in this pyramid. Half of the base of the pyramid (pink), the pyramid height(black), and the slant height (orange) form the triangle.

So our first step is to choose good prism dimensions (there are many combinations that work. The base must be square, and the product of all dimensions must be 900cm^3).

Using the 10x10x9 case, we can calculate the height of each triangular face that we need to arrive at the correct pyramid height.

We looked at how this works with an example of a cone as well.

In order to find the volume of a cone, if given the slant height, we need to use the pythagorean theorem to calculate the height of the cone first, and then we can calculate the volume of the cone after.