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Volume Between A Circular Paraboloid and a Plane

  1. Nov 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid E bounded by z = 3+x2 +y2 and z = 6.

    2. Relevant equations

    3. The attempt at a solution
    I'm going to use cylindrical coordinates. So, I have,

    z = 3 + r2

    Clearly, my bounds on z are 3 and 6. If I project the intersection of the paraboloid and the plan onto the xy-plane, I have 3 = r^2. My bounds on r are then 0 and ±√3, but I reject the negative boundary. I will use the bounds 0 and 2*pi for θ, though I don't know how these bounds are known to be appropriate. So, if I perform a triple integral of r in the order dz dr dθ, I get an answer of 9*pi.

    Does that sound legitimate?
  2. jcsd
  3. Nov 11, 2011 #2


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    Homework Helper

    The result is not correct. Show your work in detail, please.

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