Quiz Time!
Band Around The World
I saw this question in an old time book by Lillian and Hugh Lieber, probably titled Infinity. It is wonderfully counter-intuitive and points out the need to really think and analyze problems.
Band Around The World
Question 1
Earth's circumference is 24,901 miles (40,075 km). Imagine it's as smooth as a cue ball, or even smoother like a neutron star. Imagine there's a stiff tight band around it. Now if 10 feet (3 meters) is added to the band raising it up above the ground equally around the whole world could you:
Barely slip a piece of paper under it.
Crawl under it.
Walk under it.
Question 1 Explanation:
The question is really asking about the increase in radius of a circle. The circumference is equal to:
C = 2R * π
But we want to know how much higher this band is which is really asking what's the increase in radius. Rearranging the formula to find R:
R = C / (2 * π)
Let's just calculate how much radius increases with 10 feet:
R = 10 / 6.28 = 1.59'
About two feet, enough to shimmy under.
There is 1 question to complete.