Well, the circumference of the ball is C= (pi)d = 3.141... * 10 = about 31.41 cm. So when the rubber band is completely around the 10cm ball, it's length will be 31.41 cm. What I understood from the "lift the rubberband 1cm off the ball all the way around" is to increase the diameter.
If the new diameter is : 6.28 + 31.41 = pi (d)
37.69/ pi = d
There fore we can conclude that 2 cm were added to the diameter when we lift the rubber band 1cm away from the ball.
Hope this helped, now try doing the same thing using the radius of Earth.
If I am unclear on something, just tell me