The portion of the end of the cylinder covered by the liquid is called a circular segment. The area of the circular segment covered by liquid in a cylinder of radius r is given by

area = r

Multiply the segment area times the length of the cylinder to get the volume of the liquid.

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The angle is in radians.

area = r

^{2}(θ - Sin[θ])/2, where θ = 2ArcCos[(r-h)/r] and h is the height of the liquid in the cylinder.Multiply the segment area times the length of the cylinder to get the volume of the liquid.

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The angle is in radians.