Yeah, it's a tricky one. It actually requires triple integration to get the volume of the cone wedge:http://mathforum.org/library/drmath/view/65406.html
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 the line passing through the cone centers.
Since the distance of the plane intersection is just R/2, we can work out the other values with Pythagoras. We get:
cos(T) = 1/2
sin(T) = sqrt(3)/2
tan(T) = sqrt(3)
sec(T) = 2
T = pi/3
plugging them in, we get:
V = 2025.87939 cubic feet
The volume of the cone is 1/3*pi*R^2*h = 18405.5442
Therefore that shape = 2*cone - 2* wedge = 2*18405.5442 - 2*2025.87939
= 32759.3296 cubic feet.
But yeah Rhino3D is faster. Time to get an Intel Mac to run it under Windows maybe