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Integration of a cone to find centre of mass

  1. Oct 14, 2004 #1
    Can anyone help me with this question?

    A uniform solid cone of height b and base radius a stands on a horizontal table. Find an expression for the volume of the disc at height h above the base. Integrate over all the discs to show that the total volume, V, is given by V =pi/3 * b * a^2
     
  2. jcsd
  3. Oct 14, 2004 #2

    HallsofIvy

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    Start by drawing a picture. Seen from the side, the cone looks like a triangle with base 2r and height b. Now draw a line across the triangle at height h (and so b-h from the vertex). Use "similar triangles" to find the base of that triangle, as a function of h. The disk formed by the cone has that base as diameter and thickness dx. I assume you know that the voume of a disk of diameter d and thickness s is pi(d2/4)s.
     
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