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A volume integral over a sphere

  1. Mar 16, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫∫∫∇.Fdv over x2+y2+z2≤25

    F= (x2+y2+z2)(xi+yj+zk)

    2. Relevant equations

    ∫∫∫∇.Fdv = ∫∫ F.n dσ

    n=∇g/|∇g|

    3. The attempt at a solution

    g(x,y,z)=x2+y2+z2-25

    taking the surface integral and replacing all
    (x2+y2+z2) with 25
    i got
    125 * ∫∫ dσ = 12500π

    But the answer key says it is 100π
    I think i am making a mistake with numbers but, i couldn't find what is wrong.

    Thanks
     
  2. jcsd
  3. Mar 16, 2013 #2

    LCKurtz

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    Gold Member

    I don't think anything is wrong except the answer key.
     
  4. Mar 17, 2013 #3
    Hmm, ok then, thanks.
     
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