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Homework Help: Finding the number of spheres in a graduated cylinder

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    This is from a worksheet. I had to find the volume myself

    "A large number of spheres are poured into a graduated cylinder and gently vibrated until the occupy a minimum volume of 40 mL (or 40 cm^3). Use the information about close packing and the data you found to find the number of spheres in the cylinder. "

    I found -- volume = 0.0477 cm^3
    diameter = 4.5 mm
    Given -- close packing fraction = .74048


    2. Relevant equations

    Wasn't given one but I used (minimum volume) / (volume of a sphere)


    3. The attempt at a solution

    40 cm^3 / 0.0477 cm^3 = 839 spheres



    I'm not sure if I did was right. I don't know what I'm supposed to do with the information about the close packing fraction. I can't find it in my book.
     
  2. jcsd
  3. Jan 29, 2012 #2

    SammyS

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    What does the close packing fraction tell you?
     
  4. Jan 29, 2012 #3
    It tells me that 26% of the used volume is wasted space.
     
  5. Jan 29, 2012 #4

    SammyS

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    So, isn't 26% of the 40 cm3 volume, wasted space?
     
  6. Jan 29, 2012 #5
    Okay, so this is what I did.

    40 cm^3 * .74048 = 29.6 cm^3

    29.6 cm^3 / .0477 cm^3 = 621 spheres

    Is this right?

    10.4 cm^3 of the 40 cm^3 is wasted space leaving 29.6 cm^3 being used. So I would take the used value and divided by the volume of the sphere right?
     
  7. Jan 30, 2012 #6

    SammyS

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    That seems reasonable !
     
  8. Jan 30, 2012 #7
    Thanks a lot. It hit me right when I saw you said 26% lol.
     
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