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Thread: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )

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    volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )

    By using spherical coordinates , find the volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 ) , below by plane z = 0 ...


    Calculus III - Spherical Coordinates

    I'm having problem finding my Φ .... Here's my diagram ... The shaded part represent the volume bounded... i have let the limit of Φ from 0 to (π- π/4) = 3π/4 , but still couldnt get the ans volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )-dsc_0010.jpg


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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    Hey xl5899.

    I'd try finding the capped area first and then subtract it from the hemisphere volume.

    Do you know how to evaluate the volume of the cap of a sphere [In terms of setting up the limits that is]?
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    Quote Originally Posted by chiro View Post
    Hey xl5899.

    I'd try finding the capped area first and then subtract it from the hemisphere volume.

    Do you know how to evaluate the volume of the cap of a sphere [In terms of setting up the limits that is]?
    I have no problem when finding the capped area first and then subtract it from the hemisphere volume.

    But when I did the way above, I did not get the answers.....
    What's wrong with the limit??
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    Can you show your limits and working for the problem?
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    $\displaystyle \phi $ from $\displaystyle \pi /4 $ to $\displaystyle \pi /2 $
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    I'm wondering why you referred to the surface given by $\displaystyle x^2+ y^2+ z^2= 4$ as a "plane".
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    Quote Originally Posted by Idea View Post
    $\displaystyle \phi $ from $\displaystyle \pi /4 $ to $\displaystyle \pi /2 $
    why ? can you explain ?
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    Re: volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2

    Quote Originally Posted by Idea View Post
    $\displaystyle \phi $ from $\displaystyle \pi /4 $ to $\displaystyle \pi /2 $
    why ? bump
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