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Math Help - Double Integration Using Polar Coordinates

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    Double Integration Using Polar Coordinates

    Find the volume of the solid which lies inside the sphere (x^2) + (y^2) + (z^2) = 9 and outside the cylinder (x^2) + (y^2) = 4. The problem hints to use polar coordinates.
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    Quote Originally Posted by skeltonjoe View Post
    Find the volume of the solid which lies inside the sphere (x^2) + (y^2) + (z^2) = 9 and outside the cylinder (x^2) + (y^2) = 4. The problem hints to use polar coordinates.
    Well, start by drawing the two solids..
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    not to be a dick, but obviously I drew the picture.
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    bump, please help
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    Quote Originally Posted by skeltonjoe View Post
    Find the volume of the solid which lies inside the sphere (x^2) + (y^2) + (z^2) = 9 and outside the cylinder (x^2) + (y^2) = 4. The problem hints to use polar coordinates.
    you can try finding the volume of the sphere using polar coordinates/spherical coordinates or the volume of sphere formula if it is allowed, and then subtract it with the volume inside of the cylinder bounded by the sphere.

    the volume inside of the cylinder bounded top and bottom by the sphere can be found using
    these substitutions x= rcos \theta y=rsin \theta and z=z.

    then you should be able to get the answer

    (remember to use the appropriate jacobian for the integrand when using these transformations!)

    hope this helps
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