Volume of an truncated elliptical cone

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Is there a general expression for the volume of an truncated elliptical cone, that is a cone in which both the base surface and top are elliptical and not circles? Both of the ellipses are parallel surfaces if that helps. I have managed to find a general expression for a normal truncated cone at $[\frac π 3(r_1^2+r_1r_2+r_2^2)h]$. Would it be possible to approximate by using the average volume of 2 normal truncated cones calculated by using the 2 sets of radii in the ellipses?