How di I get a 2 variable function that has equal volume underneath and beneath a plane?

Im doing a math project on the optmization of the surface area of water in a cup. For this I need to plot a 2 variable function to represent the surface of the water in top of the cup when its moving. I need to implement a parameter that only plots any function that has the same volume underneath and beneath an elipsoid that represent the water surface whem its not moving. This is for the fluid to conserve it's volume. Help. By the way, the limits of the finction in the x,y axis should be in the form of a circle

[John D'Errico]

That ONLY plots ANY function with the same volume? What does that mean? What parameter are you talking about? Sorry, this makes little sense.

It appears you need to learn a bit about fluid dynamics. Not a lot. But enough to learn what shape the free surface of a fluid will take on in a rotating environment.

https://physics.stackexchange.com/questions/293106/shape-of-water-in-rotating-bucket

This is the sort of thing that entire theses have been written about of course. Certainly technical papers. I doubt you want to go into this depth:

https://link.springer.com/article/10.1007/s00707-013-0813-6

But this might be of interest:

https://www.youtube.com/watch?v=ZJ6L9mdhP30

As far as an extension of that surface into a 2-dimensional domain, that simply reduces to a rotation of that shape around the axis of rotation.

[Emilio]

@John D'Errico hellooo, thanks for the comment. Maybe I frased it wrong. I am not focusing on the movement of the water and it's physics but more on the geometry of the fluid in a static moment. What I mean by the volume is that as the fluid's shape doesn't move in the bottom and side faces of the cup. Only the top face can change its shape and surfaces area (the side canaswell butt it doesnt move on the three axis. The side face area can be calculated using line integrals and the top face using a formula for the area of a 2 variable function's surface. The only thing is as for example if the shape of the top face starts to pertrudes upwards in the center point like making the shape of when a water droplet falls in cup full of water. As the fluid in the bottom and side faces of the cup dont detach from those surfaces of the cup for the sake of the hypothetical, then to conserve the volume of the shape of the fluid (when I refer to fluid, it's less of the real thing and more of an imaginary material that can bend and change shape while conserving its volume), the top face of the fluid also has to pertrude downwards on some areas of the top surface to balance the pertrusion upwards and keep the volume constant.

Here is a drawing to demonstrate:

I dont know if that made it more or even less jjsjs. Mybe Im wrong because I don't much about the subject and if that's the case, thanks for the links, I'll be sure to revise them :)