Question

The earth is approximately circular in cross​ section, with a circumference at the equator of 24 comma 882 miles. suppose two ropes are used to create two concentric​ circles: one by wrapping a rope around the equator and another using a rope 48 ft longer than the first rope. how much space is between the two​ ropes?

Answer 1

1. find the radius of the equator. You know that the formula for the circumference is $l=2\pi r$, then

$24,882=2\pi r,\\ 12,441=\pi r,\\ \\ r=\dfrac{12,441}{\pi} =3,962.101910$ mi.

2. If you are using a rope 48 ft=0.0091 mi longer than the first rope (then the circumference is 24882.0091), then you obtain another radius:

$24,882.0091 =2\pi r_1, \\ r_1=3,962.103359$ mi.

3. The difference between radii is 3,962.103359-3,962.101910=0.001449 mi (similarly 7.65 ft)