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Surface area of a hemisphere w/ vector calculus

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    I need help proving how you could use evaluation of the surface integral [tex]\oint\oint f(x,y,z)dS[/tex] to show that the surface area of the upper hemisphere of radius a is 2[tex]\pi[/tex] a2.

    So any ideas?

    2. Relevant equations
    The teacher mentioned that the divergence theorem would be the best way to go.

    3. The attempt at a solution
    Besides the hint from my teacher, i havent gotten anywhere with the problem. It's one that has stumped my entire class. If anyone has any hints at all for where I can start with this problem, I would appreciate it greatly.
  2. jcsd
  3. Nov 23, 2009 #2


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    so start with the divergence theorem... that tranforms a volume integral, to a surface integral over the bounding surface

    so I would try setting up the volume integral first, then see if you can re-write the integrand as the divergence operator acting on a vector field... if you can do that ur pretty much there...
  4. Nov 23, 2009 #3


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    sorry read the question incorrectly, i think you would actually do it backwards from what was described
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