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Easy solids of revolution clarification

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Calculate the volume of the solid of revolution formed when you rotate region R, delimited by f(x) = x^2 from x = 0 to x = 3, around:
    a)the x axis
    b) the y axis

    3. The attempt at a solution

    I solved it using the disc method.

    a) dV = pi * x^4 * dx. thus V = (pi* x^5)/5 + c from x=0 to x=3. thus V=152.68 cubic units.

    b) since f(y) = y^(1/2), dV = pi * y * dy. thus V = (pi * y^2)/2 + c from y = 0 to y = 9. thus V = 127.23 cubic units.

    My question is: Isn´t the volume when I rotate it along either the x or y axis supposed to be the same? If it is so, I can´t find where I went wrong.
  2. jcsd
  3. Sep 14, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    No, they aren't supposed to be the same at all. Draw a sketch of the solids. They look pretty different, don't they?
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