You may have seen a puzzle / riddle where you assume that the Earth is a perfect sphere and you run a string around its diameter say one inch above the surface. How much longer is the string than the circumference of the Earth?

The answer is 2xPi inches, or 6+ inches. Yes, counterintuitive. The diameter does not matter. Hence, if you did the same with a sphere the size of a basketball, the answer would be the same.

I once used a twist on this as a little puzzle with a bit more computation. Suppose the DC Beltway of 64 miles around were a perfect circle. You and I go around the beltway at a constant 60 mph from an equal start. I'm in the inside lane and you are in the next lane, the standard 12 feet apart.

When we go around an entire lap, how far ahead am I on the inside lane?

Answer: using the logic above, you had to travel 24*Pi more feet, or about 75 feet. And since 60 mph = 88 feet per second, I beat you by less than a second after an hour of driving. Not obvious.