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Given a cylinder of radius R and height H, what is the formula for finding the volume of ​​the larger of the two geometric figures obtained by cutting the cylinder with a plane perpendicular to the bases, and placed at distance (minimum) D from the axis of symmetry of the cylinder, with R > 0, H > 0, 0 < D < R ?

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    Yes, that is what I mean. – 2011-11-09

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Area of a circular segment =area of wedge - area of triangle =$\frac{R^{2}}{2}(\theta-\sin\theta)$

angle of wedge = $\theta=2cos^{-1}{\frac{D}{R}}$

Volume=$H\frac{R^{2}}{2}(\theta-\sin\theta)$

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    "Area of Wedge" here means [Circular Sector](http://en.wikipedia.org/wiki/Circular_sector) – 2011-11-17