I am trying to figure out the formula for the volume of an object that is shaped like a donut: like a cylinder twisted into a circle and pulled back into itself. My approach is to start by thinking of the object in 2D. Take the difference of the outer circle's diameter and the smaller circle's diameter to get the distance between the outer and inner circle. Since a donut is really a bent cylinder, multiply this PI*r^2 (area of a circle). Now take this figure across the entire circumference of the donut by multiplying it by PI*d. The resulting equation I get is: Let O = outer circle's diameter Let I = inner circle's diameter Let V = volume of the donut-shaped object V = (O - I) * PI^2 * r^2 * d Anyone care to challenge this? It's important I get it right.

Let R be the radius of the torus (donut), from the center of the entire torus to the center of the curved cylinder.
Let r be the radius of the curved cylinder
Let V be the volume of the torus

V = πr2 * 2πR

HOWEVER, I think this isn't correct, so I'm going to try an integration and see what I come up with.