How is the volume of a half full cone calculated?

The simple is to calculate the volume of the cone and subtract from the result the volume of the cone whose altitude is 1/2 the altitude of the original cone. This is easier said than done. The volume of a cone with circular base is (1/3)πr2s where r is the radius of the base and s is the altitude. The radius of the base of the empty part of the cone and hence its area can be found by using the pythagorean theorem