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Math Help - Sphere/hemisphere

  1. #1
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    Sphere/hemisphere

    Sketch \sqrt{13 - x^2 - y^2}

    Attempt:

    z^2 = 13 - x^2 - y^2

    z^2 = -x^2 - y^2 + 13

    x^2 + y^2 + z^2 = 13

    Now I dont understand why this is half of a sphere (which opens up downwards) and not a whole sphere?
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  2. #2
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    If this was \displaystyle z = \sqrt{13 - x^2 - y^2}, this is really \displaystyle z = +\sqrt{13 - x^2- y^2}, which is the upper half of the sphere.

    To be a full sphere it would need to be \displaystyle z = \pm \sqrt{13 - x^2 - y^2}.
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