I haven’t read every posting but there was a previous thread about this started by yours truly:
That should help you.
Also, to see if you are doing the calculations correctly go to my website
www.1728.com/cyltank.htm
How accurately do you need this? Since you said a cylindrical tank I assume flat ends.
The Chemical Rubber Co. Standard Mathematical Tables gives this formula for the area of segment of a circle below a horizontal chord that is a vertical distance x from the center of the circle.
a = pir[sup]2[/sup] - [xsqrt(r[sup]2[/sup]-x[sup]2[/sup])+ r*sin[sup]-1/sup]
If the tank has flat ends the fraction of the total tank capacity at distances in inches up from the bottom diameter are:
Numbers to the left are inches up from the bottom and on the right are gallons.
3- 37
6- 104
9- 188
12- 285
15- 391
18- 505
21- 624
24- 747
27- 873
30- 1000
33- 1127
36- 1253
39- 1376
42- 1495
45- 1609
48- 1715
51- 1812
54- 1896
57- 1962
60- 2000
Change this sentence: "If the tank has flat ends the fraction of the total tank capacity at distances in inches up from the bottom diameter are:: to read “Gallons of fuel at distances in inches from the bottom are:”
I was going to do it in fractions of the total but Mathcad computes the volume in gallons just as easily so I did that and then forgot to change the sentence wording.
By the way. The dimensions you gave work out to a capacity of 1763 gallons if the tank is cylindrical with flat ends.
Sure, and (r-h) will change signs when h > r (i.e, when theta > 90 degrees).
Ah, so it will. Damn your close inspection!
Interesting David, that would explain why, even after emptying the tank the fuel truck never quite reached the 2000 gallon to re-fill it.
To remark on the comment to turn the tank on end… tough gentlemen, it is anchored inside a concrete catch wall (to catch leaks, spills etc)
After reading your post, I worked on google and Excel and came up with this…
=A2*((B2^2*(ACOS((B2-C2)/B2)))-(SQRT(2*(B2C2)-C2^2)(B2-C2)))/231
I think we’ve got it!
With my original fields of A,B,C,D this is a formula I set in my spreadsheet.
I made a cool graph too…
Again, with my highest education of a B+ in alegbra, reading your post are quite tough… 
OH, flat ends too…
And now to piss on everyone’s cheerios:
The wonderful calculations given above only apply if the tank is actually a true cylinder, has no dents or bulges, and is absolutely level.
To quote my calculus instructor from college:
Its a real world problem, so use a real world solution. Empty it out, and then pump fuel in and measure the depth for various volumes of fuel.