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Shell Method Question

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    The area between the y-axis and the line y = x + 1 from y = 2 to
    y = 4 is rotated about the x-axis. Use the shell method to find the
    area of the resulting solid.

    2. Relevant equations

    V = 2pi integral (radius)(height of shell) dx or dy

    3. The attempt at a solution

    Well I am kind of confused with this problem, it says to find the AREA but isn't the shell method suppose to find the VOLUME?

    Here is my attempt:

    y= x+1 -----> x=y-1

    V = 2pi integral from 2 to 4 y(y-1) dy

    I then evaluated it to get = (76/3)pi as the volume.

    What did I do wrong?
  2. jcsd
  3. Sep 11, 2010 #2


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    Science Advisor
    Homework Helper

    I'll agree with what you've done so far. The volume is 76*pi/3. If they really do want area I'd add up the area of the parts of the boundary. You've got two cylinders, a disk with a hole in it and a part of a cone. It seems like it shouldn't be too hard, but I don't know what that has to do with the 'shell method'.
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