Quote:
Originally posted by synic213
So my Granpa has this water container buried on the property of his farm. The container is a perfect cylinder, flipped on its side (the curved surface creates top and bottom, the flat surfaces form two sides). One day we sat around trying to devise a way to measure the amount of water still within the cylinder. The only access we have to the contents of the cylinder is a small hole on the top curved surface. We figured that if we dropped a measuring stick down through the hole we could measure the depth of the water (or close to it), kinda like a dip stick. So here's what we know: the depth of the water(x), the length of the cylinder(L), the diameter of the cylinder(d). Although neither one of us is a math genius, we were able to develop two equations to figure out the volume of water in the cylinder, one equation if the cylinder was less than half full, one equation if the cylinder was more than half full. I know there must be an easier way to do this (with one equation describing all possible volumes) but we couldn't figure it out. Any of you math players wanna give it a shot?
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Personally, I would measure the current depth of the water then start pumping more water into the barrel (measuring how much is added) until the barrel is either twice the starting depth (or full if it's more than half full) and then extrapolate the starting volume from the ending volume. But that's just me.