I have went to the Dr. Math site that you supplied the link for. I know that you took the equation from this site and modified it to reflect a set of cones that protrude into the center of each other. But comparing the two, I just am not followin…

The below is from a post in Feb of 2006.
Anyway, the equation for that is:
V = (1/3)*H*R^2*(T - 2*cos[T]*sin[T] + cos^3[T]*ln[sec(T)+tan(T)]).
where T is the angle between the intersection of the plane that I mentioned before and th…