I've learned in my calculus class how a function can be rotated around an axis to create a 3 dimensional shape, and the specific formulae associated with this process. What I'm wondering is whether or not this idea can be applied further (like rotating a 3D object around an axis to create a 4D object) in order to create 4 dimensional shapes, 5 dimensional shapes, etc. If so, is there a general formula for this (like volume and surface area? I've seen people do a similar process with spheres, but no general formula for any given function f(x).
Also, if there is somewhere I could learn more about this, where can I find that information?
I could be speaking nonsense.