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Cylindrical Slice (Posted on 2005-11-25) Difficulty: 3 of 5
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    
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Solution Solution | Comment 1 of 13
 
                                               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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