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Math Help - x^2+y^2+z=1 sketch

  1. #1
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    x^2+y^2+z=1 sketch

    Hi,
    I'm having difficulty with this eqatuion and wanted to know what is this equation? is it a cone? and how would i sketch the points...Thank you for your time..
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  2. #2
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    Try taking sections of it. If you plug in different values of z, what do you get in the xy plane? Are there values of z that are not allowed?
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  3. #3
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    Its actually to verify stokes theorem...x^2+y^2+z-1=0 where z is equal to or larger than 0...I just wanted to know how to sketch it and how to go about it. Thank you!
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  4. #4
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    x^2+y^2+z-1=0

    Now x^2+y^2-1=-z

    and z=1-(x^2+y^2)

    Do you know what is z1=x^2+y^2. It is paraboloid.

    Its sections x^2+y^2=k or x^2+y^2=Sqrt[k]^2 are circles with radius Sqrt[k].

    So first draw the paraboloid. Then reflect it around the z-axis (just turn it upside down), and finally move it for 1 unit up in the z-axis.

    Regards.

    P.S The graph that you need will look something like this:

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  5. #5
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    I see..thank you for making it clearer..I also have a question regarding the polar co-ordinates for a paraboloid and its boundary conditions..and also..how to convert them for the stokes theorem..Thank you!!
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