I am looking to make a triangular prism with some special properties but with no idea how to go about doing the calculations. The idea is to have the volume above each face of a triangular prism be equal if the prism was put into the smallest possible sphere.
I have taken calculus 2 and done a bit of work with derivatives and integrals, however this seems like it would require triple integration and polar coordinates, neither of which I know how to properly use.
Here is an image of the area above a surface for a cube (easier to draw a cube).
This is not an answer: it is the only way I have found to display a figure.
@Jonathon M Could you explain with the notations of the figure below what you exactly desire ? Is it the numerical value of the volume of ABCA'B'C' ? And what for (it can be interesting for us to explain your ultimate goal).