<P> Volume = h (π / 12) (((D) (D)) + ((D) (D)) + ((D D D D))) </P> <P> While this formula is more involved than the equivalent for a circle, if the major and minor axis of each ellipse are equal, the result is the more familiar formula for the frustum of a right circular cone . </P> <P> The volume calculations for these individual frustums of trunk segments can be further refined by considering the overall shape of the trunk . Tree trunks change shape, or more appropriately, curvature multiple times from base to top . It is not uncommon to see the base of a tree as neiloid in shape for 3 to 10 feet . This neiloid shape then changes to a cylinder or paraboloid for perhaps several tens of feet and then to a cone for the remaining distance . </P> <P> The best method for modeling that is to divide the trunk into adjacent segments no more than 3 to 5 feet in height / length and then apply either the cone, paraboloid, or neiloid frustum form to each . This is a labor - intensive process . To gain efficiency, longer sections can be chosen that appear to the eye to have uniform curvature . However, the longer the segment, the more important it is to choose the optimum solid . Over longer frustums, the greater volume contribution of the paraboloid or the lesser volume of the neiloid becomes apparent when compared to the basic conical form . Therefore, when modeling longer frustums the measurer needs to perform independent checks to insure that the right solid has been chosen . One way to check is to take a diameter measurement at an intermediate point and then project what the diameter would be for the chosen model at the point . If the projected diameter is substantially greater or lesser than the measured diameter, then the selected solid is not the right choice . In this case, an intermediate form that combines the two forms through weighting may be appropriate . The measurer selects weights and applies them to each solid formula to arrive at an intermediate result . Each frustum can represent a different parent cone, paraboloid, or neiloid so that there is not a need to impose a single form on the entire tree . </P>

If a volume is 10 ft.3 what does that mean