Telecom company wants to lay a cable around equator, but it turned out that the cable they've got is 1km short

Question

At what distance from the equator should the company lay the cable to compensate for their mistake in ordering shorter cable?

Answer 1

Let d = be the distance from the equator, and R = radius of the earth = 6,378 km. Then the equation to solve is:

2πR(1-Cos(d/R)) = 1 km

Since the series for Cos(x) is 1 - (1/2)x² +...., we can use this approximation and solve for d:

d = √(R/π)

For R = 6,378 km, this gets us about d = 45 km.