The World-Wide Highway
Sometimes, intuition helps us solve problems, but sometimes not. When intuition fails, math can help. What is your intuition about the following puzzle?
If we could build a road in a circle around the world at the equator, it would be about 25,000 miles long. To raise this road 5 feet above the surface, all the way around, how much longer would the road need to be?
Do you think the extra length is a little or a lot? If your intuition is failing you on this problem, don't worry. Most people have a hard time imagining situations that span a wide range of measurements, such as this case where lengths ranging from 25,000 MILES to 5 FEET are involved.
Try this experiment: jot down a quick guess that your intuition suggests is a "ballpark" answer, then see if you can find a math formula that helps, and work out an answer that way. Are the two answers nearly the same or very different? Which do you think is right? Do you still trust your intuition without question? Has your intuition changed by doing this?
Extra Credit: Jupiter's equator is about 11 times longer than the Earth's. How much longer would a road around Jupiter's equator need to be if it were raised 5 feet? Is your intuition still working?