What's the mathematic formula for the volume of a half cone?

[*Laurelindo*]

I would go along with the whole "subtract the amount you took away" routine.

Yeah, but the problem with that is that I want the formula to be completely independent on the part I subtract from it;
so that you won't have to estimate the height of that figure everytime you want to find out the volume of this bucket-figure thing.
Basically a formula that only uses variables found in the figure itself.

I tested if you could use the average area of the top and bottom and then calculate everything as if the figure were a cylinder, but that doesn't seem to work either, nor does the average of their radii (or that's what I imagine).