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...
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