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Equation of surface

  1. Jul 14, 2011 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=37177&stc=1&d=1310620954.jpg

    2. Relevant equations



    3. The attempt at a solution

    It seems very obvious that after rotation, it becomes a circle, so how to write it out mathematically?

    That I don't know the general equation of a surface.
    Is [itex]y^2+x^2=f^2(x)[/itex] the answer?


    attachment.php?attachmentid=37178&stc=1&d=1310620954.jpg
     

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  2. jcsd
  3. Jul 14, 2011 #2
    Yes, this is the general equation for a circle

    [tex]f(x)²=x²+y²=r²[/tex]

    As seen in the figure, f(x)=radius

    And from polar coordinates you can get the equation:

    [tex]x=r*cos(\Theta)[/tex]
    [tex]y=r*sin(\Theta)[/tex]
    [tex]x²+y²=r²(cos²(\Theta)+sin²(\Theta))=r²[/tex]
     
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