Rope Around The Earth Add 1 Meter

In a common version of this puzzle string is wrapped around the equator of a perfectly spherical earth.

Rope around the earth add 1 meter.

The radius of earth is 6371 km approx. From the diagram it s pretty clear it s one foot. In fact this brain teaser requires neither an exact measurement of the earth s circumference which in fact varies by many kilometers depending on which circumference you measure nor even an assumption that the earth has a circular cross sect. Suppose you tie a rope tightly around the earth s equator.

What will its height be above the surface. From there it s not hard to believe that adding 3 feet to a rope around the actual earth would raise it almost 6 inches. The string is now rearranged so that it is at a uniform height above the equator. Divide again by pi to get the earth s radius 6 370km.

Now untie the rope and add an extra 1 meter of rope and make it a perfect circle and place it around the. Imagine a rope tied around the earth s equator like a ring on a person s finger. The idea is to imagine the earth is a cube or just a square really and ask yourself if you added say 8 feet to the rope how far would that raise it above the square earth. You add an extra 3 feet to the length.

Now imagine the rope is made just one meter longer and lifted uniformly off the surface until it is once again taught. Rope around the world you have a piece of rope that just fits around the earth. If you have reasoned the answer and can t believe it you are probably right. Imagine a rope that fits snugly all the way around the earth like a ring on a person s finger.

This puzzle is somewhat counter intuitive. Now let us tie a rope tightly around its equator. Then imagine placing this longer rope back around the earth s equator. All around the earth the rope is raised up uniformly as high as is possible to make it tight again.

This string is cut and a piece 1 metre 3 ft 3 in in length is added in. How high is that.