How can one find a general volume equation for an irregular object?

Question

I want to find a general volume equation for half a water bottle that you buy at the store, and it is an irregular object. I know how to find the volume (with volumetric integration, and the water trick to see how much the water moves, and then getting an accurate result with water itself), but I want to find an equation, a general equation that I can use, to later apply to a change of rate question. Would you know how? I truly need help.

Answer 1

I don't know of any general method, but you should look up Cavalieri's Principle.