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Archimedes jumped out of his bathtub

  1. Oct 11, 2005 #1
    Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that were in Archimedes' bathwater that day, because water doesn't get created or destroyed on a large scale. It follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. In the more than two thousand years since his discovery, the water molecules from Archimedes' bathwater have been through this cycle enough times that they are probably about evenly distributed throughout all the water on the earth. When you buy a can of soda, about how many molecules from that famous bathtub of Archimedes are there in that can?
    Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is , enter 5. If your estimated answer is , you should enter 6 (rounding up to the next power of 10).

    Hint 1. Assume that the water from that bathtub is evenly mixed with the water throughout the surface of the Earth--after all, it has had more than 2000 years to do so.

    Hint 2. Avogadro's number
    There are about in 18 of water; in other words, 1 of water contains about .

    Hint 3. What to estimate
    Estimate the mass of water in Archimedes' bathtub and the total mass of water on earth. (Note that most of the earth's water is in its oceans.)

    You have do research on the worlds oceans and stuff. It sucks.

    I took like 1 hr and couldn't get it right.:yuck: Its online hw and i only have 2 attempts left.

    Thanks for the help
  2. jcsd
  3. Oct 11, 2005 #2


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    Homework Helper

    For the oceans, do a search on how deep they would be if there weren't any continents. Then use the surface area of the earth.

    Good luck.


    And think of it this way. You still have one more free guess.
  4. Oct 11, 2005 #3
    You could say that the earth is 70% covered by water and just .7(earth's surface area)
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