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?
Answer
The rope has to be 6.28 meters longer (= 2 π).
It does not even matter how big the original circle is. If you extend the the radius by 1 meter, the circle will always gets 6.28 meters longer.