Grr, you made me get my calculator out
Taking the radius of the earth to be 6378.1 km, using 2PiR you get a circumference of 40074784.21 metres. Add 1 metre, divide by Pi and then divide by two and you get a difference in radaii of:
*Drum Roll*
15.9 Cm
Do I win a cookie? = D
Correct! Well done that man. Gap between surface of the earth and the cord all around the world would be about 15.9cm. You don't need to know the circumference of the earth as it has no bearing on the answer, which is the same for any size of sphere. Distance added divided by twice Pi, so in this case 100cm/6.28 = 15.92
Amazingly large.