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Homework Help: Voulme using triple integral

  1. Jan 7, 2010 #1
    hi all

    how can i find the volume of the solid that lies within the sphere x^2+y^2+z^2=36 , above the xy plane, and outside the cone z=7sqrt(x^2+y^2) .

    your help is very much appreiated
     
  2. jcsd
  3. Jan 7, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi mhs1! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Either split it into "vertical" cylinders of thickness dr, or split it into "horizontal" discs-with-holes-in of height dz. :wink:
     
  4. Jan 7, 2010 #3
    thnx 4 ur reply

    but i didn't get it

    how can if find the boundaries
     
  5. Jan 7, 2010 #4

    tiny-tim

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    Do you mean the limits of integration?

    If you integrate over r (= √(x2 + y2)), do it from 0 to the maximum value of r.

    If you integrate over z, do it from 0 to the maximum value of z. :smile:
     
  6. Jan 7, 2010 #5
    i did the following:

    0 ≤ σ ≤ 6
    σ^2 dσ= σ^3 /3 = 72

    0 ≤ q ≤ 2π

    dq= q = 2π

    arctan 7/√50 ≤ Φ ≤ π

    sinΦ dΦ= -cosΦ= 1+cos(arctan 7/√50 )

    then i multiply them

    (1+cos(arctan 7/√50 ))*2π *72=773.8884482

    but when i enter it it gives me that it is wrong
     
  7. Jan 7, 2010 #6

    tiny-tim

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    I'm not following this at all. :confused:

    What is σ ?

    What is σ2dσ supposed to be?

    What is 7/√50 ?

    What are you trying to integrate?
     
  8. Jan 7, 2010 #7
    i'm trying to find the volume using shperical coordinate
     
  9. Jan 7, 2010 #8

    tiny-tim

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    (I would have used either cylindrical or Cartesian coordinates.)

    (and it's arctan7, not arctan 7/√50, though it is arcsin7/√50)

    ok, write it out properly this time … what is the basic formula for volume, using spherical coordinates?

    (oh, and have an integral: ∫ and a theta: θ and a phi: φ :wink:)
     
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