Why do early math courses focus on the cross sections of a cone and not on other 3D objects? Conic sections seem to get special attention in early math classes.
My question is why do these cross sections of cones deserve more attention than those of, say, a rectangular prism, a cube, or some other 3D (or any dimensional) object?
I have a couple of guesses:


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*Studying a particular "simple" example can provide insight into the general idea (i.e. cross sections of higher dimensional objects). And conic sections are deemed simple.

*The applications of ellipses, parabolas, and hyperbolas are just so vast that their graphs and properties deserve special studying (e.g. elliptical orbits).


I'd really appreciate some outside thoughts on this, even if it is just speculation. I've been giving cross sections some special study attention recently and have done a handful of google searches to try and understand why conic sections keep coming up (as can be seen in a lot of math curriculum).
Thank you!


My question is why do these cross sections of cones deserve more attention than those of, say, a rectangular prism, a cube, or some other 3D (or any dimensional) object?

Because there's nothing else. Look at the common 3D solids. The cross sections of a cuboid (and in fact any other polytope) are just a bunch of straight lines connected together, so this is just a piecewise linear graph, and piecewise linear graphs don't need to be motivated as cross-sections of three-dimensional objects. The cross sections of a spheroids (ellipsoids) are ellipses, which come up in cross sections of cones anyway. The cross sections of a cylinder are either trapeziums or ellipses. These are much less interesting and rich than conic sections!
