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Homework Help: Finding the volume

  1. Dec 26, 2005 #1
    Is there a guideline that one can follow when finding the volume of a solid obtained by revolving over a region. The three methods that i know are disk, washer, and shell method. But i dont know when to apply which method. My book doesn't explain it clearly. If anyone could help me with this, i will appreciate it. Thanking you, and have a safe and wonderful holiday.
  2. jcsd
  3. Dec 26, 2005 #2

    Depends on the symmetry of the object and how it is rotated, but you can apply both if you want. Actually, this is a good exercise...

    Check out :

    http://mathdemos.gcsu.edu/shellmethod/ I used this website when i tutored students in college. I recommend it...
    disk and shell method

    Last edited by a moderator: Apr 21, 2017
  4. Dec 26, 2005 #3


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    You could use Pappus' Second Theorem.
  5. Dec 27, 2005 #4
    thanks marlon, i will check it out.
    Last edited by a moderator: Apr 21, 2017
  6. Dec 27, 2005 #5
    I am not familiar with Pappus' Second theorem. We never learned that theorem. Thanks
  7. Dec 28, 2005 #6
    You use the disk method when you know you can distinquish a inner and outer fuction, and want to produce a glass china.
    To use the waster method, you are trying to find many A(x), to do a intergral of many A(x)dx s. you see, A(x) can have different geometries( If you were to do a disk erercise with and waster method, then A(x) is always a damn circle)
    The shell method is sort of like the waster method, but all you are doing is rotating a figure accross a given axis.
    My recommendation is to read that section 5 times, and try to understand it intuitively. My advice cannot do a damn thing for you, but it helps me to reflect more deeply.
    Last edited: Dec 28, 2005
  8. Dec 28, 2005 #7


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    http://mathworld.wolfram.com/PappussCentroidTheorem.html" [Broken]
    The theorem is very interesting, is it not?
    Last edited by a moderator: May 2, 2017
  9. Jan 2, 2006 #8

    Thanks Siddharth, Tide, Marlon, and Kant. All u guys have a Happy New Year.
    Last edited by a moderator: May 2, 2017
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