# Find the area of the larger of the two geometric figures obtained by cutting a cylinder with an axis perpendicular to the bases

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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I think that you should use term plane instead of "an axis" –  pedja Nov 8 '11 at 19:20
Could you maybe show a picture of what you want to happen? –  Ｊ. Ｍ. Nov 8 '11 at 23:34
Is this what you mean ? –  pedja Nov 9 '11 at 7:26
Yes, that is what I mean. –  Claudio Floreani Nov 9 '11 at 14:21

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