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Find an equation for the surface by rotating

  1. Sep 9, 2010 #1
    Hello, I just joined this Physics Forum, and here is my problem:

    1. The problem statement, all variables and given/known data

    Find an equation for the surface obtained by rotating the line y=3x+2 about the x-axis.


    2. Relevant equations

    y=3x+2 is the given line

    equation for flat side of cone or a circle:
    z^2=x^2+y^2 => r^2=x^2+y^2


    3. The attempt at a solution

    If you rotate this line y=3x+2 about the x-axis on a 3D coordinate system you get a cone, 2 cones pointed at each other.

    Is the "equation for the surface" meaning the circular part of the cone?

    If so, is the equation then

    |3x+2|^2

    r^2=x^2+y^2

    the r^2 in r^2=x^2+y^2 is the |3x+2|^2


    so, |3x+2|^2=y^2+z^2
    =9x2+12x+4 =y^2+z^2 ??is this the equation??

    Any help would be appreciated
     
  2. jcsd
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