Richard,
There is a nice result in geometry which says that if you take a region in the plane which has an area, a point P not in the plane and form a "tent" by joining every point on the boundary of the region to the P then the volume of the tent is
^{1}/_{3} (the area of the region at the base) (the height of the tent)
Your ovalbased cone fits this description,
and hence if you know the height you only need find the area of the oval.
If the oval is an ellipse then it has a major axis and a minor axis. Let R be half the length of the major axis and let r be half the length of the minor axis,
then the area of the ellipse is
r R
Hence if the base of your cone is an ellipse then the volume is
^{1}/_{3} r R h
Penny
