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Optimization cylindrical can Problem

  1. Nov 17, 2005 #1
    Prove that any cylindrical can of volume K cubic units that is to be made using a minimum of material must have the height equal to the diameter.
     
  2. jcsd
  3. Nov 17, 2005 #2

    Tom Mattson

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    Hi,

    I've moved your thread to the homework help section. In order to receive help you must show how you started this problem.

    Thanks,

    Tom
     
  4. Nov 17, 2005 #3
    all ive got so far is 2(pi(1/2x)^2)+(x^2pi) and all that explains is the area of any can given the height/diameter. But i dont know how to prove it with calculus.
     
  5. Nov 17, 2005 #4

    Tom Mattson

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    Your equation doesn't make any sense to me. For starters it only has one variable, but it should have two.

    Let [itex]d[/itex] be the diameter and let [itex]h[/itex] be the height. Can you state expressions for the total volume [itex]V[/itex] and the total surface area [itex]S[/itex] in terms of [itex]d[/itex] and [itex]h[/itex]?

    If so then you're almost home.
     
  6. Nov 17, 2005 #5
    there is no reason to seperate d and h from eachother because they are the same value d=h=x

    and the equation for volume is (pi)r^2x
     
  7. Nov 17, 2005 #6

    Hurkyl

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    No they are not:

    (1) Firstly, the diameter of a cylinder is an entirely different thing than the height of a cylinder.

    (2) Secondly, nothing in the optimization problem even (directly) suggests that d and h should be equal... it says that the answer should have d and h equal.


    If you're still confused by (2), consider this analogy:

    You are asked to prove or disprove that the only solution to the equation [itex]x^2 + 3x + 2 = 0[/itex] is [itex]x = 2[/itex]. How would you do it?
     
  8. Nov 17, 2005 #7

    Tom Mattson

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    *thumps head*

    You're supposed to show that, not assume it!

    OK, how about surface area? You're going to need that, too.
     
  9. Mar 21, 2010 #8
    ok so the whole point of this problem is to solve everything and then compare d to h in the end

    so the surface area being 2pi*r*h + 2pi*r^2, would you find the derivative of this and set it equal to 0?
     
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