Ring Around the Earth, Plus Some

A timeless puzzle:

Imagine you have a rope with a perfect length to wrap snuggly around a perfectly spherical earth (the circumference of earth is approximately 24,859.82 miles (40,008 km)). Now imagine the length of the rope is extended just 10 feet and again wrapped around the earth (supported so it keeps it tautness and doesn't fall).

What is the size of the gap between the earth and the rope?

If you haven't heard about this before or run the math, you'd probably think an extra 10-feet would make no noticeable difference to a rope wrapped around the entire circumference of the globe. But, guess what?

Just an extra 12 feet on almost 25,000 miles would be 1.6 feet off the ground around the entire circumference of the globe.

To make things even stranger, compare that with a string pulled tight around the circumference of a baseball and then extend it by 10 feet. Surprise! It would also be 1.6 feet off the ground. Counterintuitive, but true.

Here's how to do the math: