Question:

If we tie a rope around the equator and measure its length, it will be ~ 24,818.58 miles long. If we raise the rope 1 foot above the Earth at the equator, how much longer will the rope need to be for both ends to touch?

Options:

1. 6.28 feet
2. 24.82 miles
3. 6.28 miles
4. 248.2 miles
5. I don't know

Solution:

The earth radius is about 6400 km.So the diameter of earth is about 12800 km.The earth has not an exat spherical shapes. So it's equatorial radius is 6.378*10^6 m or 3963 mi and it's pole diameter is 6.357*10^6 m or 3950 mi and the radius of a sphere as volume as earth is 6.37 *10^6 mi or 3600 mi .

Circumference is 2 * Pi * radius.

3950 * 2 * 3.1415926535897932384626433832795 = 24818.581963359366583854882727908 miles

24818.581963359366583854882727908 * 5280 = 131042112.76653745556275378080335 feet.

If we raised the string 1 foot above the earth how much longer would the sting need to be in order for both ends to touch?

Calculate new radius.
3950 * 5280 + 1 = 20856001 foot radius

New circumference is:

2 * 3.1415926535897932384626433832795 * 20856001 = 131042119.04972276274234025772864 feet

Subtract the new circumference from the original for your answer:
131042119.04972276274234025772864 - 131042112.76653745556275378080335 = 6.2831853071795864769253 feet.

Answer:
6.28 feet