Teaser 2

This has been one of my favourites for a while…  If you built a monorail around the equator, 1 mile above the ground, how much longer than the earth's circumference would it be?

Answer

2π (that's just over 6¼) miles. (Of course, I've assumed the earth is a perfect sphere.)

Explanation

At first, it looks as though some crucial information is missing: for example, the radius or diameter of the earth. As it happens, though, the answer is the same however big the planet is.

Suppose the radius of the earth is r miles. Then its circumference is 2πr miles.

The radius of the monorail will be r+1 miles, so its circumference is 2π(r+1) miles. This can be expanded to 2πr + 2π miles.

So, the difference between the two circumferences is 2πr + 2π − 2πr, i.e. 2π, miles.