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 Cylindrical Slice (Posted on 2005-11-25)
A right cylinder has height h and radius r. It is sliced by a plane that is tangent to one circular base at A and intersects the other at diameter BC. What is the volume of slice ABCD?

Note that BO=CO=DO=r, AD=h, BC is perpendicular to DO, and AD is perpendicular to DO.

 See The Solution Submitted by Brian Smith No Rating

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 Solution | Comment 1 of 13
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`                                               h                     -- r  -- sqrt(r^2 - x^2)  -- - y                  |     |                   |  r                  |     |                   | Slice Volume = 2 |     |                   |    dz dy dx                  |     |                   |                  |     |                   |                 -- 0  -- 0                -- 0`
`                                                                -- r  -- sqrt(r^2 - x^2)                   |     |                                  h |     |                               = - |     |                  2y dy dx                r |     |                                    |     |                                  -- 0  -- 0     `
`                                                                -- r                    |                                     h |                                  = - |  (r^2 - x^2) dx                r |                                        |                                      -- 0  `
`                2              = - h r^2                3 `
`                `

 Posted by Bractals on 2005-11-25 11:02:15

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