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Need help finding the minimum surface area of a cylinder?

  1. May 3, 2015 #1
    Member warned about posting without showing an effort
    1. The problem statement, all variables and given/known data

    'Using the graphing function on your Graphics Calculator, or otherwise, determine the radius for a minimum Surface Area.' I HAVE NO IDEA WHAT TO DO??????????????

    2. Relevant equations


    3. The attempt at a solution
     
    Last edited by a moderator: May 3, 2015
  2. jcsd
  3. May 3, 2015 #2

    ehild

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    Welcome to PF!

    Type in the whole question, please. What else is given for the cylinder?
    If nothing else is given, the minimum surface area belongs to zero radius, but I do not think that is the expected answer.
     
  4. May 3, 2015 #3
    Hi!
    I have to do this for 3 different cylinders, and I've been given the volumes of each of them; 447.97cm, 153.94cm and 446.73cm.
     
  5. May 3, 2015 #4

    ehild

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    Well, you know the volume. How is it related to the radius r and the height h? What is the surface area in terms of r and h?
     
  6. May 3, 2015 #5
    I've worked the surface area of each of the cylinders to be (in terms of r only, as this is what was asked)
    169.39cm
    164.93cm
    992.17cm
     
  7. May 3, 2015 #6

    ehild

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    How did you get those numbers?
     
  8. May 3, 2015 #7

    Mark44

    Staff: Mentor

    Since the OP has not provided a statement of the problem or any efforts toward solving it, I am closing this thread.
     
  9. May 3, 2015 #8

    Mark44

    Staff: Mentor

    Somewhat reluctantly, I'm going to reopen this thread. @Sharni Kelaart, this -- "I HAVE NO IDEA WHAT TO DO??????????????" -- does NOT constitute an attempt at a solution. In future posts, please make more of an effort to fill out the homework template.
     
  10. May 3, 2015 #9

    ehild

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    Sharni,

    The rules here require that you explain what you think about the problem. You gave three numbers in your last post as result, have you got them from a plot on a graphing calculator? What was you plotted?

    Next time when you start a thread obey the rules. Write the full text of the problem statement, write the formulae which can be relevant, ( they would be the volume and surface area of a cylinder here) and show what you think about a possible solution. In those equations, you have two variables, the radius r and the height h. You can eliminate one (h) and then you get a function, the area in terms of the radius. If I understand your post correctly, that was what you did and input the calculator. But the numbers are not correct. I would like to see that formula.

    I hope to see you again soon.

    ehild
     
  11. May 4, 2015 #10
    I don't know if you're still looking for help but...

    Surface Area = 2πrh + 2πr2
    Volume = πr2h

    We have volume, but two unknown variables, radius and height.

    Do you see how they are to be related?

    We have to solve for h with the volume equation, then plug that h into surface area equation. I hope this is helpful. If you still don't get it, refer to this page: http://www.math-prof.com/Calculus_1/Calc_Ch_17.asp
     
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