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

[*Laurelindo*]

Let's say we have a cone, and then we cut away the top of it so we get a shape similar to a bucket - how do you write the volume formula for this?
I thought it would be very easy to find out, just subtract the volume of the part you cut away from the volume of the cone as it looked in the beginning - but I always manage to get the height from the part I cut away into the equation.
I suppose trigonometry would make this easier, but I'm not sure how to use it here.