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Math Help - volume of half ball mmn 15 4a

  1. #1
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    volume of half ball mmn 15 4a

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  2. #2
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    I suggest you switch to spherical coordinates as soon as possible. Review the section in your book on spherical coordinates. In particular, you should know how to describe half a sphere and that the Jacobian in spherical coordinates is J(r, \theta, \varphi)=r^2\sin\theta. In this case you'll have 0\leq \theta\leq \pi/2 (assuming the ball is as you've graphed it).

    Spherical coordinate system - Wikipedia, the free encyclopedia
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  3. #3
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    i tried to solve it like this but i got a bad resolt where is my mistake?
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  4. #4
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    Quote Originally Posted by transgalactic View Post
    i tried to solve it like this but i got a bad resolt where is my mistake?
    There is a miscommunication between the two of you. Mondreus is you theta as the azimuthal angle, but you are using phi as the azimuthal angle.

    This is a common problem depending on which books you are reading
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  5. #5
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    where is my mistake why i get 0
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  6. #6
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    TheEmptySet told you where the error lies. I used the symbols from the Wikipedia article where a unit sphere is 0 < r < 1, 0 < \theta < \pi, 0 < \varphi < 2\pi.

    You have switched the limits for \theta and \varphi.
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  7. #7
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    i disagree
    0 < \varphi < \pi/2
    not 2 pi
    correct?
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  8. #8
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    I was referring to the unit sphere.

    What you posted is only correct if the Jacobian for the spherical coordinates in this problem is r^2\sin\varphi. Again, read the Wikipedia article I linked to if you're confused about the symbols used.
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