Pyramid vs Cube

Make a pyramid that looks like this:

square pyramid square pyramid

You can print out this template to help you:

Pyramid Net

Now make two more exactly the same, so we have three:

square pyramid three off

Fit them together and we get a cube:

square pyramid two joined   square pyramid three joined

So three of those pyramids exactly make one cube!

And so the volume of that pyramid is exactly one third of a cube.

Pyramid Perimeter and Height

We can extend that idea to come up with the volume of a general pyramid:

Volume = 1 3  × [Base Area]× height

cone dimensions h=height, r=radius, s=side length

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!