1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Volume of a solid of revolution

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid that results when the region bounded by the curves y=16-x[tex]^{2}[/tex] and y=16-4x is revolved around x=8.

    If you could show me how to do it with both the shell method and washer method it would be greatly appreciated.

    2. Relevant equations



    3. The attempt at a solution

    When trying the shell method i tried to shift the graph to the left 8 units and then revolving it about the y axis and got:
    y=16-(x+8)[tex]^{2}[/tex] and y = 16-4(x+8) which gave me


    2[tex]\pi[/tex]*[tex]\int^{-4}_{-8}[/tex]x(16-(x+8)[tex]^{2}[/tex] - (16-4(x+8))) dx

    and that gave me a negative answer so I know that can't be right
     
  2. jcsd
  3. Feb 17, 2010 #2

    Mark44

    Staff: Mentor

    I would suggest working with the graphs as they are. Your way could work, but seems prone to errors that might not otherwise occur, and doesn't really simplify things that I can see.

    If you use washers you will need to solve each of your equations for x in terms of y. The volume of a typical volume element is
    pi(R^2 - r^2)dy

    For R, the larger radius, measure from the vertical line to the x value on the slanted line. For r, the smaller radius, measure from the vertical line to the x value on the parabola. For example, R = 8 - <x value on slanted line>. And similar for r, the smaller radius. Since R > r, then R^2 > r^2, so you'll get a positive value for V.

    Using shells, the volume of the typical volume element is
    2*pi*R*(y val on parabola - y val on slanted line)*dx. R is the radius of the shell, measured from the line x = 8. If you measure it the right way you should get a positive value for V.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook