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Finding surface area with volume

  1. Sep 19, 2012 #1
    Ok, so I did a test today for advance functions and there was a question: the volume of a pop can is 350ml, find the minimum surface area and determine the dimensions.
    Where I got stuck:

    350=pi(r)^2*h
    h=350/pi(r)^2

    SA= 2pi(r)^2+2pi(r)(h)
    SA= 2pi(r)^2+2pi(r)(350/pi(r)^2)

    =(2(pi(r)^3+350))/(pi(r))

    I'm stuck here :S
     
  2. jcsd
  3. Sep 19, 2012 #2
    How do I [STRIKE]shot web[/STRIKE] er, minimize function? Doesn't it have to do with the derivative having a certain value?
     
  4. Sep 19, 2012 #3

    chiro

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    Hey ahmedb and welcome to the forums.

    One thing you should be aware of is that volume is cubic metres (or centimetres or inches or some other unit of length) so you need to convert the liquid quantity to volume by looking at the density.

    As Muphrid pointed out above, you want to look into finding a minimum which has a direct correspondence to the derivative being zero.
     
  5. Sep 19, 2012 #4
    This problem has nothing to do with density. You simply need to find the minimum value for the surface area function you came up with. To do this, you find the derivative of your SA function with respect to r, and set it to 0.
     
  6. Sep 19, 2012 #5

    chiro

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    If you want things in the right units, this is a critical step.
     
  7. Sep 20, 2012 #6

    Mark44

    Staff: Mentor

    ahmedb,
    Homework problems should be posted in the Homework & Coursework section, not in the math technical section.

    I am moving your post.
     
  8. Sep 20, 2012 #7

    HallsofIvy

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    No, it isn't. Liquid quantity is volume. Nothing in this problem has anything to do with density, weight, or mass.
     
  9. Sep 20, 2012 #8

    chiro

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    Yeah you're right: I was under the impression that it was in another unit. My apologies.
     
  10. Sep 20, 2012 #9

    HallsofIvy

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    Happens to me all the time!
     
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