How about this one:
let's assume the Earth has the form of a perfect sphere (no hills or mountains, no flatness near the poles etc) with radius r = 6400 km.
Now you go to a certain point on equator and stick a pole in the ground. Then you tie a thread around the base of the pole (zero elevation from ground). Then you start a long journey around the world, following the equator, unrolling the thread. When you get around the world back to the starting point, this means you have unrolled exactly the length of thread corresponding to the circumference of Earth at elevation zero.
Now you unroll an additional 1 meter of thread.
The question: for what distance should this thread be lifted uniformly from the ground level all around the world so that the 1-meter extended thread would end exactly at the pole? Or with other words, for what amount should the radius of Earth be increased for the length of the extended rope to be exactly the circumference?
First go with your instinct and then do the calculation!