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Math Help - Volume involving a triple integral

  1. #1
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    Volume involving a triple integral

    Find the volume determined by z less than or equal to 6-x^2-y^2 and z greater than or equal to sqrt(x^2+y^2).

    I'm not sure how to find the limits of integration for this question. I set the two inequalities to each other and found that x^2+y^2=9 and x^2+y^2=4, but am a little stumped on where to continue from there. I'm thinking at some point I will need to convert to cylindrical coordinates, but am still not sure how to go about it. Any help would be appreciated.
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  2. #2
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    In cylindrical the equations are z=6-r^2 and z=r. These intersect in the circle r=2.

    So in cylindrical, we have 0\leq \theta \leq 2\pi , 0\leq r\leq 2 and r\leq z\leq 6-r^2.
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  3. #3
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    Thanks so much! I ended up getting 32pi/3, which I hope is right!
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  4. #4
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    Yep - that's what I got.
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