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Use polar coordinates to find the volume of the given solid.?

z = sqrt(x^2 + y^2)

x^2 +y^2 = 81

1 Answer

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  • rotchm
    Lv 7
    2 years ago
    Favorite Answer

    First, sketch it. Note that this is a cone. Assuming you want the volume inside it:

    The element of volume is dx dy dz = r dr dθ dz in polar coords. So, evaluate

    ∫∫∫ r dr dθ dz.

    Now for the ranges. θ obvious. r & z depend on each other.

    Note that r = √(x² + y²) thus your cone is z = r. That is, given r, z goes from r to √81 = 9.

    2π..9......9

    ∫......∫......∫ r dz dr dθ. Can you take it from there?

    0....0......r

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