I once heard the following statement:
Take a piece of string and measure the length around a ball. Now add 1 meter to the string and stretch it out evenly around the ball. Obviously the diameter/radius will increase. Not sure by how much though.
Do the same thing for a ball the size of the earth. Add 1 meter to the string and (amazingly, at least to me) the increased radius/diameter is the same for a ball the size of the earth as for a small ball held in your hand.
Is this true? If yes, why is this true and by how much is the radius extended?