# Height of liquid in a horizontal cylinder

Hi

I am trying to calculate the height of liquid in a cylinder.

I know the dimensions of a cylinder and the volume of liquid.

I know how to calculate the volume for a given height, but i cant flip the equation to get the height.

volume = area * length;
area = r2(θ - Sin[θ])/2, where θ = 2ArcCos[(r-h)/r]

So that goes that

area = volume/length.

How can i isolate the height from the area calculation? I don't think it's possible because it relies on trig and calculating the dimensions of a triangle based on the height of liquid and the radius of the cylinder.

If it is not possible to isolate that height, is it possible to work it out another way without iterating over every possible height until i come to the actual volume specified.

My maths level is high school and that is 10 years ago so i dont remember ever calculating anything like this.

Thanks
Ben Crinion