This roughness affects the amount of slack needed, as might be expected. Not only does it bulge out around the equator, but mountains and valleys give it a rough surface. It should be noted that the Earth is not a perfect sphere. Hence, this 2ПЂ extension would be the same for a ball, planet, or star of any size. Also, because the value of R earth was not any number in particular throughout this proof, the answer didn't depend on the specific radius of the Earth in any way. 2, which yields an increase of 2ПЂ no matter what the radius of the ball is. Indeed, one can see that the additional 2ПЂ is a result of distributing the 2ПЂ in Eq. The new length of the rope is merely 2 ПЂ feet longer than the original length. Lengthening the rope so that it is 1 foot off the ground at all points simply means changing the radius of the circle it forms from: R rope 1= R earth to R rope 2= R earth+1 ft. The puzzle states that we have to lengthen the rope and made the rope hover 1 foot of the surface of the earth. When the rope is taut around the globe, its length equals the circumference of the Earth. R earth is the radius of the Earth and the original radius of the rope (R rope 1).R rope 2 is the radius of the circle made by the extended rope.C earth is the Circumference of the Earth and the original length of the rope (L rope 1).L rope 2 is the length of the extended rope.

Earth point measure polygon