Assume that the Earth is a perfect sphere whose circumference at the equator is 25,000 miles, and suppose a piece of rope has been made that exactly encircles the Earth at the equator. If an additional yard is added to the rope, how far above the Earth will the new rope stand? Express your answer to the nearest hundredth of an inch.
inches
To figure out the answer, determine the radius of the circle now formed by the rope, and subtract from the radius of the circle before. Setting that up as an equation results in:
(25,000 miles + 1 yard)/2π − (25,000 miles)/2π
Perhaps somewhat surprisingly, the terms representing the circumference of the Earth cancel each other out, and the result is 1/2π yards, or about 5.73 inches. Since the size of the Earth doesn't factor into the end result, this answer would be the same no matter how large or small the rope was in the first place.
