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The theorem is v=(A

*base*x h)/3, where "h" is the perpendicular height.

The proof, or what I think it is, is:

Consider any pyramid, perpendicular height "h" and with area of base "A"

I believe, you then split the pyramid into n layers. Let n be the unknown number of layers and k be the layer you are measuring. So, by similarity the kth layer will have a base with dimension k/n as a fraction of the original base, right? Then the area of the base would be (k/n)squared x A.

The area of the base of each layer will be (1/n)squared x A, (2/n)squared x A,..., (n/n)squared x A.

That's about all I have so far.

I'm not quite sure how that works out; my friend taught me it, so I don't totally understand it. Like what does it mean "by similarity the kth layer will have a base with dimension k/n as a fraction of the original base"?