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Homework Help: Cylindrical coordinates

  1. May 4, 2009 #1
    1. The problem statement, all variables and given/known data
    Identify and sketch the graph of the surface y^2 + z^2 = 1. Show atleast one contour perpendicular to each coordinate axis

    2. Relevant equations

    3. The attempt at a solution

    for the yz plane z = (1-y^2)^1/2 a circle of radius 2 centered at the origin

    xy, set z=0 yields y = +/- (1)^1/2 which is a straight line at y+ and y-

    xz, set y = 0 yields z = +/- 1^1/2 which is a straight line at z+ & z-

    i do not get what the 3d model should look like
  2. jcsd
  3. May 5, 2009 #2


    Staff: Mentor

    No. For the y-z plane (IOW, x = 0), you have y2 + z2 = 1, which is a circle of radius 1, centered at the origin.

    Solving for z was really a wasted effort, since this is the equation of a circle.

    What does "straight line at y+ and y-" mean? In the x-y plane you have y = +/- 1, two horizontal lines
    Same comment as above.
    What you need are more cross sections, such as the cross section in the planes x = 1, x = 5, x = 10, x = -1, x = -5, and x = -10. After you understand why I picked these cross sections, and graph a few of them, you'll have a good idea of what this surface looks like.
  4. May 5, 2009 #3
    but there is no x value in the function.
  5. May 5, 2009 #4


    Staff: Mentor

    Which means that it is arbitrary; you can choose any value for x.

    A clue that you're dealing in three dimensions is that they asked for the surface. If the problem had asked you to graph the curve y2 + z2= 1, you would have needed only two dimensions.
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