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Problem with conversion/ order of magnitude

  1. Sep 1, 2008 #1
    1. The problem statement, all variables and given/known data
    One cubic centimeter (1.0 cm3) of water has a mass of 1.0 multiplied by 10-3 kg.
    (a) Determine the mass of 1.0 m3 of water.

    (b) Assuming biological substances are 98% water, estimate the masses of a cell with a diameter of 1.0 µm, a human kidney, and a fly. Take a kidney to be roughly a sphere with a radius of 3.3 cm and a fly to be roughly a cylinder 3.3 mm long and 1.2 mm in diameter. (Type your answer using one of the following formats, 1.2e-3 for 0.0012 and 1.20e+2 for 120.)

    2. Relevant equations

    Volume of a sphere - (4/3) * pi * radius^3
    Volume of a cylinder - pi * radius^2 * height

    3. The attempt at a solution

    I believe I am erroneously making the assumption that there should be 100 cubic centimeters in 1 cubic meter. As such, my proposed answer to A was 1.0E-1

    It is in fact 1.0E-3
    Please clear up this conversion issue for me.

    On to the other problems:
    I believe if I can get assistance with one, I can figure out the rest.
    I have been told to assume 100% water in the calculations of these masses, so never mind the 98%.

    Cell Problem: [(4/3)*pi *0.5^3 ] = .5236 *1.0E-3 kg= .005236
    So I'm at 5.24E-6 kg for the weight of this cell

    The correct answer should be 5.24e-16 kg/cubic centimeter. I am obviously confused over something fundamental. Any help would be much appreciated.
  2. jcsd
  3. Sep 1, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    There are not 100 cubic centimeters in a cubic meter. There are 100 x 100 x 100 cm3 in a cubic meter. Where you're going wrong with the others are with units. You can't just stick a 0.5 in for the radius since your question is giving the diameter of the cell in micrometers.
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