Calculating the volume of an Elliptical tank, where the top and bottom ellipse are different sizes

Question

I need to calculate the volume of an Elliptical tank/tube, where the top and bottom ellipses are different sizes. I have done some research and have only really found formulas for calculating an Elliptical tank where the top and bottom are equal. Any help would be appreciated, if the answer could be posted in a way thats easy for me to read as im not too math savvy with all the symbols etc (i understand pi, pow etc...)

This is the kind of object im trying to calculate the volume from Elliptical Tank but where the two ellipises are different sizes

This is the geometry that im trying to calculate the volume of

Answer 1

Are you looking for the volume of an elliptical truncated cone? if so

See this link: https://keisan.casio.com/exec/system/15374075528834

Answer 2

We have that the surface area for an ellipse is give by $S=\pi ab$ therefore if we know how $a$ and $b$ are vary along the axis $z$ we have

$$V=\int_0^H S(z)dz=\pi \int_0^H a(z)\;b(z)\; dz$$