I see..Based on the image I guess the cutting plane should intersect the floor of the cone at the outer edge of the base.
The angle will still depend on the height/radius ratio but that dependence is trivial.
One assumes the intersection of the tilted plane with the z=0 plane forms a line which is expected to be tangent to the base of the cone. And one assumes a right circular cone.Still it depends on the orientation of the plane then. Is the line of cut of the tilted plane with the z=0 plane the x=0 line, the y=x line? there are y=nx solutions...
That is better, and h'<h is the reason your previous approach didn't work.Yes, ##
π.a.b.h'/3 = π.h.r^2 /6 ## where h' is the height of the perpendicular drawn from the apex of the cone to the oblique cutting plane and h,r the height and radius of the original cone is the correct formula to be used!