I have been attempting to find the volume of an Elliptic truncated cone by dividing it into cross-sections of elliptical cylinders and then stacking them up. I got the idea from the integration of the truncated cone but am not able to continue with the method as there are 3 variables involved. Could someone please guide me through the process that I am supposed to do?
The cone:
The cross section:
Extend the sides of the cone upward in your imagination until they meet and form a phantom "full cone" and a phantom "small cone" on top of the elliptic cone frustum. The volume of the frustum is the volume of the phantom "entire cone" minus the volume of the phantom "small cone". Here are examples with other frusta: