Basically I have a horizontal tank with elliptical heads on each end. Given any liquid height, I would like to calculate the surface area which is in contact with the liquid. The heads can be represented by a general oblate spheroid described by equation (x2 + y2)/a2 + z2/c2 = 1. I can compute the partial surface area for z=XXX to YYY by taking the surface of revolution about the z-axis (ie for a vertical tank). However how can I calculate the partial surface area for x=XXX to YYY? I am not looking for a closed form equation, just something I can numerically integrate.