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Homework Help: Solid of Revolution Problem

  1. Dec 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the volume obtained by rotating the solid about the specified line.

    y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.

    2. Relevant equations

    I used the disk method

    3. The attempt at a solution

    I drew a sketch and used disk method. For the radius I used 2-(1/2)x with a height of 1, and integrated. For an answer, I came up with 5pi/4. Does this seem correct? Thanks!
     
  2. jcsd
  3. Dec 29, 2011 #2


    I am getting a different answer. What are your bounds? What is the integrand?
     
  4. Dec 29, 2011 #3
    My bounds were from 1 to 2.
     
  5. Dec 29, 2011 #4
    That is correct. What about the integrand?
     
  6. Dec 29, 2011 #5

    SammyS

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    What do you mean by "with a height of 1" ?

    What function did you integrate?
     
  7. Dec 29, 2011 #6
    Sorry, I don't know why I typed height, I meant to say that that the bounds were 1 to 2. For the integrand I just had pi*2-(1/2)x*1 dx
     
  8. Dec 29, 2011 #7
    The area of one of the disks is going to be [itex]\pi \cdot (2 - \frac{1}{2} x)^2[/itex]. What happens when we sum those disks from [itex]x = 1[/itex] to [itex]x = 2[/itex]?
     
  9. Dec 29, 2011 #8
    I think I forgot to square the radius when I originally did it. I redid the problem and came up with 19pi/12. Is this still wrong?
     
  10. Dec 29, 2011 #9
    That is the answer I got.
     
  11. Dec 29, 2011 #10
    Awesome. Thanks guys!
     
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