Does the trucker have a computer? I came up with two ways of doing the problem, but for both I ultimately needed a computer to reach the final solution.
Method 1:
I used some trig and came up with the following formula:
{5/9*pi*cos-1((10-h)/10)} - {2*(10-h)*sqrt(20*h+h^2)} = 25*pi
I used the Goal Seek tool in Excel (basically plug this formula into cell A2 and h into cell A1, then tell it to set A2 equal to 25*pi by manipulating the value of h in cell A1) to find a solution to this equation.
With this method I got an answer of
8.04.
Method 2:
A horizontal "slice" of a vertical (circular) cross-section of the cylinder has an length of sqrt(20*h + h^2). If these "slices" are integrated from zero to x (with x being the height filled with gas) and this is set equal to 25*pi, solving for x will provide the solution.
I plugged this function into
"The Integrator" and got some crazy ass function spit out at me. I guess I could plug this function into Excel and solve the same way as I did in my first method, but I don't feel like it.
...in any event, there is probably a ridiculously easy way to get the answer to this problem that I didn't think of. You probably didn't want us to use a computer anyway. [img]/forums/images/icons/smirk.gif[/img]
-- Homer