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Surface area formula proof - integrate circumference of volume of revolution

  1. Nov 19, 2011 #1
    1. The problem statement, all variables and given/known data
    I believe this is intended to be a proof of the formula πrl, surface area of a cone.


    2. Relevant equations
    A complete volume of revolution gives you a cone - the height h is the x value on a graph, the radius r is the y value. The y intercept is zero, therefore y=r/hx . All integration is with lim h→0


    3. The attempt at a solution
    When I tried this, I got:
    ∫2πydx
    =2π∫r/hx dx
    =2πr/h∫x dx
    =2πr/h ∫x2/2
    =πrh! So why has this not worked? I need this to give πrl!
     
  2. jcsd
  3. Nov 20, 2011 #2
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