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Math Help - How long is the rope?

  1. #1
    A riddle wrapped in an enigma
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    How long is the rope?

    You have a rope that will reach around the earth (+/- 40,000 km). If you put sticks of 1 meter high around the world and lay the rope on these sticks, how much longer will the rope need to be?

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  2. #2
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    haha well I had a quick shot at it, and my answer feels wrong so I will post it and have someone explain....

    I have the circumference of the earth in metres as 40,000,000
    > diameter<-40000000/pi
    > diameter
    [1] 12732395
    so the diameter of this earth is 12732395

    I am adding 1 metre stick to each radius, and 2 to the diamter and times by pi to get the new circumference;
    > (diameter+2)*pi
    [1] 40000006

    giving 6 extra metres, which seems crazy...
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  3. #3
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    Ah thinking about it, each extra unit diameter gives me Pi units extra circumference, so the answer is 2 Pi metres extra?
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  4. #4
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    Quote Originally Posted by tolland View Post
    Ah thinking about it, each extra unit diameter gives me Pi units extra circumference, so the answer is 2 Pi metres extra?
    Assumption: The Earth is a sphere

    Let r be the Earth's radius such that r = 4 \times 10^7m

    Let the stick be \delta r

    Take a small bit of "width" of the Earth and let it tend to 0 so that it can be ignored giving a 2D model.

    The original circumference of the circle is C_r = 2\pi r = 8\pi \times 10^7 whereas the new area of the circle would be 2\pi (r+ \delta r) = 2\pi (4\times 10^7 + 1) = 8\pi \times 10^7 + 2\pi

    The difference would be 2\pi \: m
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  5. #5
    A riddle wrapped in an enigma
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    Excellent!

    You know the strange thing is, it doesn't even matter what the radius of the great circle is. The rope will always be 2\pi \ \ or \ \ 6.28 units longer if the radius is increased by 1 unit.

    C=2\pi r

    C=2\pi(r+1)

    C=2\pi r + 2\pi
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