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Most efficient cost for a cylinder

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data
    An open-topped cylinder is to have a volume of 250 cm3. The material for the bottom of the pot costs 4 cents per cm2, and the material for the side of the pot costs 2 cents per cm2. What dimensions will minimize the total cost of this pot?

    3. The attempt at a solution
    $$
    A_{bottom}=πr^2
    \\
    C_{bottom}=4(πr^2)
    $$

    $$
    A_{side}=2πrh
    \\
    C_{side}=2(2πrh)
    $$

    $$
    V=πr^2h
    \\
    250=πr^2h
    \\
    h=\frac {250}{πr^2}
    \\
    ∴C_{side}=2(2πr\frac {250}{πr^2})
    $$

    $$
    C_{total}=4(πr^2+2(2πr\frac {250}{πr^2})
    \\
    \frac {d(C_{total})}{d(r)}=8πr-\frac{1000}{πr^3}
    $$

    Then I tried to use the first derivative test. I am stuck.
     
    Last edited: Apr 28, 2013
  2. jcsd
  3. Apr 28, 2013 #2
    Uhh I messed something up there with itex.
     
  4. Apr 28, 2013 #3
    I really messed up the formatting in that first post so it kind of looks like a mess. Until I figure that out, perhaps someone could point me in the right direction to solving the question?
     
  5. Apr 28, 2013 #4
    Okay I think I fixed all the formatting. Silly me.
     
  6. Apr 28, 2013 #5
    NEVERMIND. I figured out my silly error. It's all good now. Can I delete this thread?
     
  7. Apr 29, 2013 #6

    Mark44

    Staff: Mentor

    We don't delete threads as a matter of course. Even though it's of no use to you now, others might find it helpful.
     
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