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Title text: The local police, building inspector, and fire marshal are all contesting my 'safety' assertion, or would be if they could reach me past all the traps.

If those lines are equally spaced but the shape is a pyramid, then each section wouldn't be 20%, although I'm not sure of the easiest way to work out what it would be.

The easiest way to calculate it would be to assume that it is a square pyramid, with the height of each section being one unit. Unfortunately, we still need one more measurement, the easiest of which would be to assume the side angle at 45°. With that, that will give us the length of one side of the pyramid with some simple geometry (a 45/90/45 triangle has the same height as base length, and as we're measuring height at the center of the pyramid, the length of the base is simply twice the height) From there, we get the volume of each section: 1.333... cubic units for the capstone, 9.333 for the second layer, 26.333 for the third layer, 49.333 for the safety layer, and 91.333 for the lowest layer.

Safety comes out to be approximately 29.6% of Cueball's needs.

It never says that the percentage of his needs corresponds to the volume of the pyramid. Maybe part of the issue is that 48.8% of the volume of the pyramid is dedicated to only 20% of his needs (at the bottom), whereas another 20% of his needs only get 0.8% of the pyramid.

(Also I'm pretty sure you don't need to know the angle to get the percentage; anything that depends on it will just end up cancelling out.)

It's been many years since I took a geometry class.