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Math Help - Triple integral: finding volume(with attempt)

  1. #1
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    Triple integral: finding volume(with attempt)

    Triple integral: finding volume(with attempt)-volume_of_bounded_sphere.png
    Plz have a look on the image I uploaded above to see my question.
    I tried to solve the question, and come up with two thoughts.
    I must have some wrong intuitions, I used to think method 1 and method 2 will have the same answer, but actually they don't.
    Which of the integrals, dz, dr or dθ is incorrect?
    and what is the correct boundary?
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  2. #2
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    Re: Triple integral: finding volume(with attempt)

    Hey happymatthematics.

    There is a simpler method using rotation of volumes since z = b is aligned with the axes: do you have to use one technique over another?
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  3. #3
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    Re: Triple integral: finding volume(with attempt)

    hi chiro.
    I've solved the problem with the technique of cylindrical coordinate(r,Θ,z).
    but I don't know how to deal with this problem with spherical coordinate(ρ,Θ,φ).
    could you desmonstrate how to do it in spherical coordinate? or tell me the range of φ and then let me try.
    Thank you.
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