How is the volume of this pyramid obvious? The corner of a unit cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. The chopped of part is a pyramid. The source says the volume of the pyramid is obviously $\frac16$. I don't understand how this is obvious. Can someone help me visualize this?
I don't want a proper proof because I can also do that ie find the area of base and height and volume is $\frac13$ × base area × height.
I want someone to help me visualize the result as to why this is obvious that the volume of the chopped off pyramid is $\frac16$th of the volume of the cube.


The $\sim$ symbols indicate equivalences in volume due to Cavalieri's principle. The $\cong$ symbols indicate congruences; the solids in the bottom row are the chopped-off pyramids of the question. Thus half a cube has the volume of three such pyramids, and the full cube has the volume of six.
