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Finding volume of arch dam

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data

    The problem is number 4 at this link: http://college.cengage.com/mathematics/larson/calculus_early/2e/students/downloads/mws6a.pdf

    The axis of revolution is 150 and the rotation is 150 degrees.

    2. Relevant equations

    Using the shell method.

    My offset is x+220.

    The equations that make up the cross section:

    [tex].03x^2+7.1x+350[/tex]

    [tex]-6.593x+389[/tex]

    [tex]389[/tex]


    3. The attempt at a solution

    I planned on splitting the cross section into three parts, which are the 2 triangles and rectangles, and apply the shell method on each of these. So first I did [tex]2pi*Integral[(x+220)(.03x^2+7.1x+350)][/tex] with the bounds being -70 to -16. Then I multiplied this answer by (150/360) since it's only 150 degree rotation. In each of my applications of the shell method, the p(x), or the distance to the axis of revolution stayed at x+220. Am I on the right track if I do this for each of the 3 sections?
     
  2. jcsd
  3. Oct 8, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Sentral! Welcome to PF! :smile:

    (have a pi: π and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

    I'm not sure what you're doing (what's 220? :confused:) …

    the shell method involves finding the volume of the arc-shaped slice (it will be 150/360 of the volume of a complete cylinder) from x to x + dx …

    it will be something times dx …

    and then integrating. :smile:
     
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