A rope around Earth equator need only 2 meters more in length to rise 31cm from equator. Radius of Earth at Equator = R
Circumference of Earth at Equator = C
C = 2 × pi × R
So using calculus, we can see how much C changes when R changes (we don't need to know the actual radius of Earth at Equator):
dC = 2 × pi × dR
So if dR = 31
Then dC = 2 × pi × 31 = 194.779....
So 195cm or 1.95m is more accurate though.