Pyramid vs Cube
Make a pyramid that looks like this:
- It has a square base
- Its apex (top point) is directly above one corner
- Its height (the distance from that corner to the apex) is the same as the base length
You can print out this template to help you:
Now make two more exactly the same, so we have three:
Fit them together and we get a cube:
So three of those pyramids exactly make one cube!
And so the volume of that pyramid is exactly one third of a cube.
We can extend that idea to come up with the volume of a general pyramid:
Volume = 1 3 × [Base Area]× height
And, by thinking that a cone is just like a pyramid with a ridiculous number of sides, we can come up with the volume of a cone:
Volume = 1 3 π × r2 × h
Isn't mathematics wonderful!