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Cylinder radius and height

  1. May 6, 2014 #1
    1. The problem statement, all variables and given/known data

    A closed cylinder is required to have a volume of 40m^3 but made with the minimum amount of material. Determine the radius and height the cylinder must have to meet such a requirement.

    V= πr^2h

    Steps needed:

    a) Insert value and transpose for h
    b) Then sub into the area formula
    c) Then differentiate

    2. Relevant equations

    V= πr^2h

    3. The attempt at a solution

    V= πr^2h
    40= πr^2h
    40/h= πr^2
    h=πr^2/40

    A= 2πrh+2πr^2 Subbing in h= πr^2/40
    A= 2πr(πr^2/40)+2πr^2
     
  2. jcsd
  3. May 6, 2014 #2

    SammyS

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    What's your question?


    Now you need to do step c.
    c) Then differentiate.​
    Then a little bit more.
     
  4. May 7, 2014 #3
    I expanded the brackets and got 2πr^2+80r^-1

    And differentiated that to 4πr-80r^-2 Is that correct?

    After that how would I go on to find the radius r?
     
  5. May 7, 2014 #4

    SammyS

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    The answer to that is related to "What is the reason for differentiating?" .

    When you solved

    V = 2πr2h

    for h, you made a mistake.

    What you have is actually 1/h .
     
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