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'Mathematically Similar' Question

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  1. Mar 13, 2016 #1
    1. The problem statement, all variables and given/known data
    314476b.jpg

    2. Relevant equations


    3. The attempt at a solution
    I tried cross multiplying but obviously that is not the case. These types of questions are the ones I always lose marks in. Any help would be appreciated.
     
  2. jcsd
  3. Mar 13, 2016 #2

    mfb

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    How do volume and surface area change if you make an object twice as long/high/thick?
    Based on that, what is the scale factor in your problem?
     
  4. Mar 13, 2016 #3
    I'm not sure how to find out, I'm really sorry. All I know:

    volume of larger container : volume of smaller container
    3456 : 1458
    Simplified:
    64 : 27

    Which is where I got stuck. I don't know what to do from there.
     
  5. Mar 13, 2016 #4
    If working with weird flask shapes makes you uncomfortable, try doing the same with two cubes. As long as the two bodies are mathematically similar, it shouldn't matter to us. See if that helps.
     
  6. Mar 13, 2016 #5

    PeroK

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    Another hint:

    If the ratio of volumes is 64:27, and if you think the ratio of surface areas should be 64:27, do you think the ratio of heights should be 64:27 as well?
     
  7. Mar 13, 2016 #6

    mfb

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    And to make an extreme example: an adult human has about 3 to 4 times the height of a newborn baby. How would an adult look like with 3 to 4 times the mass of a newborn baby?
     
  8. Mar 13, 2016 #7

    epenguin

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    And once you get the principle, noticed that some arithmetical simplifications are offered in the numbers given you. (They could even point you the way, but not unambiguously.)
     
  9. Mar 14, 2016 #8

    epenguin

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  10. Mar 14, 2016 #9
    God @mfb ! Now that visual isn't leaving my head for the next two hours.

    I hope the OP understood.
     
  11. Mar 14, 2016 #10

    mfb

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    I thought about using the opposite direction but that didn't make it better.
     
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