The "multiply by 2pi" version of this problem is the one where you have to lift the rope by a cat's height all around the entire earth. So if you have an army

The "multiply by 2pi" version of this problem is the one where you have to lift the rope by a cat's height all around the entire earth. So if you have an army of southern-hemisphere cats and they need to get to the northern hemisphere, but you have cunningly put a rope around the equator because you don't want dogs to invade, how much extra rope do you need to lift it to just let in the cats but not the dogs? (I'm assuming all cats are shorter than all dogs.)