"Cy Galley" wrote:

If you can find the area of the ends and average them, then multiply it by
the average distance between them, it will give you the volume.

That's an excellent approximation, and is probably what I would use
for a calculation in my head or on the back of an envelope. But the
actual formula is just about as easy with a calculator or spreadsheet.

actual formula (assuming ends in parallel planes, I believe) is 1/3 *
h *(b1+b2+sqrt(b1*b2)), where b1 and b2 are the areas of the bases.

Your formula is exact if b1=b2. If one end is 4 times the area of the
other (twice the linear dimensions), your formula overstates the
volume by about 7%. If one end is twod=ce the area of the other, it
overstates the correct answer by less than 2%. So the bases don't have
to be very close in size for your approximation to give pretty good
results.

As a worst case, your approximation approaches a 50% overstatement as
the shape gets close to a "pyramid" in which one end has zero area.
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