Area of a sphere = 

A

=

4

π

r

2

Area between the latitude, or 

A = 2*pi*r^2*(1-cos(theta))

1 - cos(theta) = 1 m. km^2 / (2*pi*r^2)

theta = arcos(1 - 10^6 km^2 / (2*pi*r^2) ), r = circ/(2*pi) = 40,000/2/pi = 6366.2 km

theta = arccos(1 - 10^6/2/pi/6366.2/6366.2) = arccos(1 - 0.003026988008686) = arccos(0.996073011991313) = 0.080877478519613

0.080877478519613/pi*20,000 km = 514.9 km