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?
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
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;
giving 6 extra metres, which seems crazy...
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