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Hardcore rotation problem in multivariable calculus

  1. May 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Let C be the circle defined by (x-2)2+y2 = 1. If this circle is rotated along the y-axis, a torus will form. What is the Cartesian equation for the torus?

    3. The attempt at a solution

    The solution manual says you just switch the x in (x-2)2+y2 = 1 with r=√(x2+z2) and simplify.


    Why would that work? Why does the x in the first equation equal the radius of the torus? I don't get it.
     
  2. jcsd
  3. May 21, 2013 #2
    help?
     
  4. May 21, 2013 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Nikitin! :smile:

    if (x,y,z) is on the torus, then so must be (√(x2+z2),y,0)

    but that must be on the original circle, so (√(x2+z2) -2)2+y2 = 1 :wink:
     
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