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Problem with finding volume using shells

  1. Mar 26, 2015 #1
    A solid is generated by revolving the region bounded by y=(1/2)x2 and y= 2 about the y-axis.
    So what I did is set up my integral V= 2pi (integral sign from 0 to 2) x(1/2)(x)2 dx
    When I solve i get 4pi, and then I have to find the radius of the hole which has one fourth of the volume. So the volume of the hole is pi ( the hole is centered around the axis of revolution which is y-axis). Then I set equal integral from 0 to r (the radius of the hole ) is 2pi(1/2)(x3)dx = pi. the answer i get is 41/2, which is not right as i checked
    Last edited: Mar 26, 2015
  2. jcsd
  3. Mar 26, 2015 #2


    Staff: Mentor

    This appears to be a homework problem or one in a textbook. @asadpasat, please start a new thread in the Homework and Coursework section (Calculus subsection). This forum section is for conceptual calculus questions, not for homework problems.
    Last edited: Mar 26, 2015
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