Quote:
Originally posted by synic213
Wow guys! Thanks for the long and glorious equations! I will have to try them out to see if any of them hold water (pun intended). The thinking behind my equations went something like this: If the water level is less than half the barrel, you can determine the chord length of the water level, and from that draw a triangle from the center of the "circle" to the chord tips, in essence giving you a pie piece. Subtract the area of the triangle from the entire area of the pie piece (calculated by computing the ration of angles between piece of pie to whole pie) and you're left with the cross sectional area of the water. Multiply by the length of the cylinder and you have your volume. This equation didn't work when the barrel was more than half full because the water was now on the opposite side of the chord, if that makes sense. For this scenario, we had a set value for the volume of water for a half full barrel, and then added in the amount of water sitting on top (using a method similar but not identical to equation 1). I'll try to rederive the equations if I can, but they were all done using simple geometry and trig. I'm sure there's away to describe the whole circle at once, using calc, which is probably what you guys did. Thanks again.
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No, I suspect none of us used calculus. You see, in order to have used calculus, I would have had to find the integral of sqrt(r^2 - (r - x)^2), which is not an easy task!
No, we all used the same goemetric approach, as I suspected, and that's why I pressed you for your actual formulas (and why I'm still surprised you haven't posted them). You see, it would actually be a bit of a trick to find a formula that didn't work for both cases. Ours works because, if the barrel is more than half full, we would be subtracting a
negative triangle and, thus, we would be properly adding it.
So, again, I would be rather suprised if your formula didn't work for both cases...