Fun & Games Puzzel...

Discussion in 'General Chat' started by Metalman, Apr 19, 2015.

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  1. Metalman

    Metalman Well-Known Member
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  2. rkw

    rkw Well-Known Member

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    I say 20 cm.

    My explanation below. Skip past this if you still want to work it out yourself.




    1. First, reduce the problem. The string goes around the circumference 4 times on a 12 cm length tube (rod). That's the same as 1 time around a 3 cm length tube, and multiply by 4 for the final answer.
    2. So we start with a tube of 4 cm circumference and 3 cm length, and the string goes around it once.
    3. Now imagine that we cut the tube lengthwise between where the string begins and ends. Unroll the tube. You will get a rectangle of 3 cm (tube length) x 4 cm (tube circumference)
    4. On this rectangle, the path of the string going around the tube 1 time is from one corner to the opposite corner.
    5. The string is the hypotenuse of a right triangle with 3 x 4 sides. Applying the Pythagorean theorem, the hypotenuse (string length) is 5.
    6. Multiply by 4 to get the final result 20.
     
  3. ScottinBend

    ScottinBend Space Cowboy
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    Bingo^^^^^^^^

    Nice. This was actually part of a test I took some years back.
     
  4. Metalman

    Metalman Well-Known Member
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    #4 Metalman, Apr 20, 2015
    Last edited: Apr 20, 2015
    Krikey... I misread the circumference for the diameter... It pays to read the instructions first...

    It's a 3,4,5 triangle as you pointed out...:D
     
  5. mrntd

    mrntd Well-Known Member
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  6. rkw

    rkw Well-Known Member

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    But for 4 cm diameter, I get 51.678.

    4 * sqrt( (4 * pi)**2 + 3**2 )

    As the problem said, "Show your work".
     
  7. Eric@Helix

    Eric@Helix New Member
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    ^Whelp^ You're smarter--and better educated--than I am.
     
  8. MCS02

    MCS02 Moderator
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    [ame="https://www.youtube.com/watch?v=NO0cvqT1tAE"]https://www.youtube.com/watch?v=NO0cvqT1tAE[/ame]
     
  9. Metalman

    Metalman Well-Known Member
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    My reasoning was the string had to do two things...
    Go around the rod 4 times and reach to the end of the rod

    Pi x D =12.566 x 4 of them = 50.265 + 12 (length of rod) = 62.265cm

    But my reasoning was flawed...
     
  10. DneprDave

    DneprDave Well-Known Member
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    The length of the string is the length of the diagonal of the rectangle with

    l = 4 \cdot 4 cm = 16 cm\ and\ w = 12 cm

    Therefore the length of the string is

    s = \sqrt{16^2 + 12^2} = 20\ cm
     
  11. rkw

    rkw Well-Known Member

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    Damn... so that's why the piece from my machinist came back looking kinda funky. :D
     
  12. Metalman

    Metalman Well-Known Member
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    Gave the same quiz to my daughter... She processed the answer the same as what you used and told me the answer was 20cm....:Thumbsup:
     
  13. Savvy

    Savvy Well-Known Member
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    Smart kid.
     

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