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Doughnut Volume

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data
    x^2 + y^2 = a^2

    A circle with radius a and at the origin (0,0) is rotated around x=b (b is greater than a). Find the volume of the doughnut it creates as it is rotated.


    2. Relevant equations



    3. The attempt at a solution

    I'm unsure if I'm doing this right, but I did this:

    1) Break the circle into 4 pieces. One piece of the circle becomes the square root of (a - x^2). I plan on multiplying the whole thing by 4 later.

    2) V = [pi (b)^2 - pi (b - sqrt (a-x^2)^2]dx ----- outer - inner

    3) V = [pi(b^2) - pi(b^2 - 2b*sqrt(a-x^2) + a - x^2)]dx

    4) V = pi (b^2 - b^2 +2b*sqrt(a-x^2) - a + x^2)dx

    This is what I have so far. Can anyone tell me if I'm doing it right so far, and if I did anything wrong, please correct me.

    Thanks, and sorry if this is hard to read.

    EDIT: Forgot to add the interval will be from ∫ 0 to b
     
  2. jcsd
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