Band Around The World

Quiz Time!

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:  
A
Barely slip a piece of paper under it.
B
Crawl under it.
C
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.
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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.