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Simple word problem.

  1. Oct 23, 2005 #1
    Question: A rectangle with a perimeter of 40cm is rotated around one of its sides, creating a right cylinder. What is the largest possible volume for this cylinder?
    Here's what I have done so far:
    Equation #1:
    40 = 2h + 2r
    r = 20 - h
    Equation #2:
    Volume = pi*r^2h
    = pi(20-h)(h)
    = 20pi*h - h^2*(pi)
    Derivate of volume: 20pi-2pi*h
    10=h
    Therefore, r also equals 10.
    Thus, the maximum volume is 3141.592cm^3, which is incorrect.
    The actual answer is 3723.37cm^3. Any help would be great. :biggrin:

    Sorry, but I think this should be in the "Calculus and Beyond" board.
    I'm not too sure how to move it there, though.
     
  2. jcsd
  3. Oct 23, 2005 #2

    I think you forgot to square the radius (20-h) when putting it in....

    I may be wrong, I just looked at it quickly and that's what I saw.

    EDIT: My way, my calculator now tells me 3723.3691 so yup, that was your mistake
     
    Last edited: Oct 23, 2005
  4. Oct 23, 2005 #3
    Thanks for the help, I really appreciate it.
    I'll be more careful next time. :smile:
     
  5. Oct 23, 2005 #4
    I have another question, wouldn't it be more appropriate if the "restraint equation" was 40 = 2h + 4r rather than 40 = 2h + 2r. It just seems to make more sense since if the cylinder is transformed into a rectangle, each side of the triangle would be a diameter (or two times the radius) rather than just the radius, which we are assuming right now. I'm just curious to know why I get the wrong answer if I do it the way that seems to be more logical to me.
     
  6. Oct 24, 2005 #5

    HallsofIvy

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    I assume you meant "rectangle" where you wrote "triangle" above. The reason a side of the rectangle is a radius not a diameter is that the rectangle is rotated about one side, not about a center line of the rectangle.
     
  7. Oct 24, 2005 #6
    Ah, I understand it now! Thanks for clearing that up.
    I think the key to the question is that it is rotated to create a right cylinder.
     
  8. Feb 28, 2008 #7
    what did you get for your "r" value? I'm doing somethign wrong...
     
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