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Extrema physics problem

  1. Jan 18, 2006 #1
    A cylindrical can is to hold 20 m3. The material for the top and bottom costs
    €10/m^2 and material for the side costs €8/m^2. Find the radius r and height h of
    the most economical can.

    the answer is h= 5 and j=2

    i have found the eqn such as v=pi j^2 h =20 pi

    and 2pi j^2 + pi j h = 18...then i don't know how to do.....pls help
     
  2. jcsd
  3. Jan 18, 2006 #2

    berkeman

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    Staff: Mentor

    Have you learned yet how to use differentiation to find maxima and minima of a function?
     
  4. Jan 18, 2006 #3
    ya..........but is my eqn correct??
     
  5. Jan 18, 2006 #4

    berkeman

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    Staff: Mentor

    What's "j"? Where's "r" in the equations?
     
  6. Jan 18, 2006 #5
    j = radius
     
  7. Jan 18, 2006 #6

    berkeman

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    Staff: Mentor

    Well, anyway, I'd solve it this way:

    -- write an equation 1 for V = f(r,h)

    -- write an equation 2 for A = f(r,h)

    -- rearrange equation 1 so you can substitute it into equation 2 to eliminate r in equation 2.

    -- differentiate the result with respect to h, and set the result = 0

    -- solve for the height h that minimizes the area, and then use equation 1 to solve for r.
     
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