Using revolutions of a solid I derived a function relating the volume of liquid within a sphere with the height of that fluid within the sphere. However it is a cubic function which I don’t know how to swap the dependent and independent variables. I’ll try to explain better my problem.
V=(pi/3)(3rh^2-h^3)
It’s clearly easy to determine the volume at a given height. My problem is that solving for height for a given volume is an ugly cubic. I have resorted to using a Newton approximation to solve for height. Which works but is a bit tedious and a ‘new approximation’ equation must be used for each different volume. In short, is there a way to transform this V(h) function into a h(V) function?
V=(pi/3)(3rh^2-h^3)
It’s clearly easy to determine the volume at a given height. My problem is that solving for height for a given volume is an ugly cubic. I have resorted to using a Newton approximation to solve for height. Which works but is a bit tedious and a ‘new approximation’ equation must be used for each different volume. In short, is there a way to transform this V(h) function into a h(V) function?