Results 1 to 10 of 10

Math Help - Disks, Washers, Shells and Confusion

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    9

    Disks, Washers, Shells and Confusion

    Hello Everyone,

    I'm currently taking a calculus 2 course and I don't really understand the differences between the disk method for finding the soild of revolution and the washer and shells methods. I gather that the shells method is easier when you are rotatating around the y axis and disk is better when rotating around the x axis. Washers seems to be good for when there will be a hole in the object that you are rotating. My problem is that I don't really know how to use these methods and have been stuck for hours now trying to apply them.

    Thanks a lot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Your post borders upon asking for a tutorial and we are not a tutorial service.
    If you will post a specific question telling us what you do not understand, then perhaps someone can help.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    No, those rules will not get you very far. Each method is better when it is. The very best method is the one you understand. It would behoove you to practice both.

    Let's see what you have.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2011
    Posts
    9
    Thanks for the quick replies. I have x-y^2=16, x=20 rotated about x=0. I set y^2 +16=20 and solved for the roots and got \pm2. I then integrated \pi x (y^2 +16)^2 dy. The correct answer is 5888\pi/15 and I have 18112\pi /15. Is my logic correct? I've checked and double checked my work and I can't find a mistake which leads me to believe that I'm doing something wrong in the setup.

    Thanks again
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,125
    Thanks
    1009
    washers about the y-axis, taking advantage of symmetry ...

    V = 2\pi \int_0^2 20^2 - (y^2+16)^2 \, dy
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2011
    Posts
    9
    Do you also have to solve the corresponding integral from -2 to 0 and add the results together?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,125
    Thanks
    1009
    Quote Originally Posted by CanadianEngineering View Post
    Do you also have to solve the corresponding integral from -2 to 0 and add the results together?
    note the 2\pi in front of the integral ... as stated, I took advantage of the graph's symmetry.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    May 2011
    Posts
    9
    Ah, I was also confused by the 2\pi part, thanks a lot
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    May 2011
    Posts
    9
    Got the answer, thanks so much Skeeter!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Or...

    4\cdot\pi\int_{16}^{20}x\cdot\sqrt{x-16}\;dx

    More symmetry creates the slightly unusual value on the front.

    Excellent example. Which do you perceive as easier or more useful? It masy be one or the other for this problem, but a different choice on the next.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume by Disks/Washers
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 11th 2010, 08:14 AM
  2. Cylindrical Shells (Little on Disks too)
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 26th 2009, 02:15 PM
  3. help with volume: disks and washers
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 19th 2009, 01:10 PM
  4. washers vs shells
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 16th 2008, 09:45 PM
  5. Help with integration using disks or shells
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2008, 04:18 PM

/mathhelpforum @mathhelpforum