Let's assume the Earth has radius R. Then the circumference, i.e., the equator, has the length
L = 2 pi R
where pi = 3.1415926.... So the rope has the length L m.
Now we want to increase the radius by 1 m. This gives a new length for the rope, L':
L' = 2 pi (R + 1 m)
What we want to know, is how much our rope must be extended: what is the difference between L' and L?
Difference = L' - L = 2 pi (R + 1 m) - 2 pi R = 2 pi m
Here we have the answer: it's sufficient with another 6.2 m!
If you look carefully at the calculation, you find that the result does not depend on the radius R! You can do this with any radius R you like.
![[ Earth ]](./earth2.gif)