To preface, I am a poor undergrad who's only in Calculus 1. Instead of studying for my final exam, I decided to test my knowledge by writing a program that calculates Riemann Sum approximations of areas under curves between two points on a graph.
Naturally, I thought this was pretty cool and sent it to a friend who's a Stats PhD with a math B.S. His response was to try and adjust the program to find the volume of a Torus with r=1. I have no idea how to approach this, but I am not one to back away from a challenge.
So far, my knowledge of Riemann sums is obviously on a 2D plane with the form
$$A = \Delta x[f(x_0) + f(x_1) +...f(x_n)]$$