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Math Help - Volume Word Problem (geometry-type problem for physics)

  1. #1
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    Volume Word Problem (geometry-type problem for physics)

    We're doing reviews of what we learned in chemistry in physics at the moment. (We just began our new semester so we changed our classes.) This was group work and my group and I were wondering if what we got as our answers was correct.

    problem:

    There are two questions stemming from the problem. I have the work we did after them, then what we did and any questions. I'd be very grateful if someone could help us out. (:

    questions:
    1) What would be the total volume of all the adults in the world?

    (There's supposed to be an 'e' after the 1.0, so it should read 1.0e^-1. Sorry for the mistype.)


    Are we correct in our scientific notation in the first place? Even though it's .10, we'd have to move the decimal because the coefficient has to be between 1 and 10 was our logic. Then, we used the rules of exponents and got our answer of 2.0e^8. We simply placed m^3 back because it's the volume.
    Our logic for the work was that the volume is 1.0e^-1, so multiply that by the 2.0e^9 because that's how many people are.

    2) Compute the length of one edge of a cubic container that has a volume equal to the volume of all the adults in the world.


    *Cube is supposed to read as container in the picture below. I suck at typing sometimes! :P

    Okay, we're pretty sure we botched this up horribly. Maybe it was a bad idea to put three soon-to-be English majors in a group together? ;] Regardless, our logic is shown at the top in the green outlined box. We know that the volume of the cube and the volume of the people are the same. We assumed that the container was a cube, also. To get the volume of the container, we would have to cube all the sides.
    So, from there, we figured the length of an edge would be the cubed root of the volume of the people. Our answer approximated to 5.9e^9 m^3.


    Thanks for any help and I'll be back to answer any questions you have for me about what we did.
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  2. #2
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    (2.0 \times 10^8 \, m^3)^{\frac{1}{3}} = 5.8 \times 10^2 \, m
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  3. #3
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    Volume problems

    Hello deeskato

    Your answer to part (1) is fine, although your use of scientific notation isn't quite right. In standard index form (scientific notation) it should read:

    Total volume = (1.0 \times 10^{-1}) \times (2.0 \times 10^9)

    = 2.0 \times 10^8 m^3

    (Note: if you're using a spreadsheet or a scientific calculator, this will appear as 2.0E8.)

    In part (2) your formula for the length of one edge of the cube is correct:
    \sqrt[3]{2.0 \times 10^8}

    But your answer isn't right (and the units are m, not m^3). Did you use a scientific calculator for this? The correct answer is approximately 5.85 \times 10^2, or 585 m.

    Grandad
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