Thread: 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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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...

Ah thinking about it, each extra unit diameter gives me Pi units extra circumference, so the answer is 2 Pi metres extra?

Originally Posted by tolland

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

Let the stick be

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 whereas the new area of the circle would be

The difference would be

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 units longer if the radius is increased by 1 unit.