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
Ouch.

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

.