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How many drops in all the oceans?

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Simple question, but I don't know how to correctly approach it.

    How many drops of water are in all the oceans on earth? Assume that 1cm^3 contains 25 drops of water.


    2. Relevant equations

    The average depth of the ocean is 4 km. I know I will have to convert to cm.
    Radius of Earth: 6400 km
    About 70% of the earth is covered by oceans.


    3. The attempt at a solution

    Need help setting up the problem correctly.
    I've tried various things. I'm not sure if I have to use the surface area of a sphere or the volume of a sphere.

    I have to subtract the depth of the oceans (4km) from 6400km...?
     
  2. jcsd
  3. Sep 10, 2009 #2

    mgb_phys

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    Find the surface area of the earth, then take the proportion of this that is covered by water.
    Then imagine unrolling this areas as a flat map, not find the volume of a slab of water of this flat area and 4km high.

    Then convert km^3 to cm^3
     
  4. Sep 10, 2009 #3
    mgb_phys,
    by doing what you advised, I obtained a surface area of 5.15 x 10^8 km^2 times .70, which gave me a total of 3.6 x 10^8 km^2 roughly.

    3.6 x 10^8 km^2 times 4 km for the depth gives me a volume of 1.44 x 10^14 cm ^3 (once I conver to cm).

    Am I missing something? Because this is not the correct answer.

    The question is asking me for the amount of drops of water. I should be multiplying my final answer, 1.44 x 10^14 cm ^3, by 25 (1cm^3 = 25 drops).

    Where am I making a mistake?
     
  5. Sep 10, 2009 #4

    ideasrule

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    1 km^3 = (1 00 000 cm)*(1 00 000 cm)*(1 00 000 cm)=10^15 cm^3, not 10^5 cm^3.
     
  6. Sep 11, 2009 #5
    Oops. I see what I did wrong.

    Thanks to both of you!
     
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