Partial cone calculations? (1 Viewer)

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Imagine that I have a pipe that is on a constant slope at any percent. On the low end of the pipe, there is a container filled with water. The water has naturally found a leveling point up into the pipe. Provided the level of water in the container is above the top of the pipe, a portion of the pipe will be completely filled with water. Out certain distance, the pipe will go from being completely filled to partially filled (where the top of the pipe is higher then the level of water) How can i find the volume of water that is contained in the part of the pipe that is not completely filled. The best way that I can picture this is a cone that has been laid on its side so that the center of the base, and the point of the cone are level, and partially filled with water. The cone volume is simple, but the partial cone problem is beyond my mathmatical knowledge. Any help would be beneficial to me.
 

Tide

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From your description, I don't see how a cone picture applies.

Isn't it more like a cylinder with a plane cutting through it? You would be interested in the volume contained between the top and bottom points of intersection within the cylinder.
 

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