Around the World

How much rope do you need to circle the Earth?

The circumference of the Earth is 40,076 km (24,902 mi). Let’s say we had a rope that long and used it to circle the Earth, like the red line in the picture. For purposes of this puzzle, assume that the Earth is a perfectly smooth sphere, with no hills or mountains, and that the rope floats on the oceans, which have no waves.

Now let’s raise the rope up on poles that are each 1 m (3.3 ft) long, as shown by the yellow lines in the second picture, which is not drawn to scale.

This path will be longer. How much more rope do we need?

Course:

Geometry [1]

Result/Solution(s)

Solution: Around the World Math Puzzle

We need only 6.28 m (20.6 ft) more.

The radius of the circle has increased by 1 m. The circumference of a circle is 2pr , where r is the radius. So if the radius increases by 1 m, the circumference increases by 2p x 1. With p = 3.14, 2p x 1 = 6.28.

Here's another question. If we circled the Sun, whose circumference is 4,400,000 km (2,734,032 mi) with a rope the same way and then raised it on 1-m-high poles, as we did with the Earth, how much more rope would we need?

Geometry puzzle [2]