Answer to Question #21247 in Abstract Algebra for Hisham wadi
Let R - radius of the cylinder, h - the height of the liquid level, L - thelength of the cylinder.
Denote S - square circle segment occupied by water.Then the volume of fluidis V = S * L.It remains to calculate S.
1. if h is less than R
denote b = 1 - (h / R)and the half-angle of the segment occupied by thewater relative to the cylinder
a = arccos (b)Then S = R * R * (a-b * sqrt (1-b))
2. h if more R
denote H = 2R-h,then calculate the amount of the remainder without water Swt
denote b = 1 - (H / R)and the half-angle occupied by the remaining segmentsof the cylinder without water
a = arccos (b)Then Swt = R * R * (a-b * sqrt (1-b))and S = pi * R * R-Swt
Volume is V=S*L
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