Math Trivia : Rope around the earth
How long does the rope go away from the earth if I add a rope with the length of 6m to the rope which is rolled around the earth?
Assume the radius of the earth is 6,400km and Pi is 3 for calculation.
Answer
1 m
The length of the circumference of the earth is 6400 km × 2 × Pi = 12800 km × Pi.
This is the original length of the rope and when 6 m is added, it is 12800 km × Pi + 6m.
The diameter of the earth is calculated as (12800 km × Pi) / Pi + 6m /Pi = 12800km + 6m / Pi.
Since Pi = 3, 12800km + 6m/pi = 12800km + 6m/3 = 128000km + 2m.
The radius is half of diameter or 6400km + 1m which means the rope goes away (float) 1 m from the earth.
1 m
The length of the circumference of the earth is 6400 km × 2 × Pi = 12800 km × Pi.
The diameter of the earth is calculated as (12800 km × Pi) / Pi + 6m /Pi = 12800km + 6m / Pi.
Since Pi = 3, 12800km + 6m/pi = 12800km + 6m/3 = 128000km + 2m.
The radius is half of diameter or 6400km + 1m which means the rope goes away (float) 1 m from the earth.
