Physics HELP?!!? The earth has a diameter at the equator of 7926 miles. Look at detail for rest of question?

Question

i have no clue how to do this question...

The earth has a diameter at the equator of 7926 miles. Imagine a string wrapped around the equator of a perfectly smooth earth. Suppose we now add 15.0 feet to the length of the string and shape the longer string into a smooth circle with its center still at the center of the earth. How far will the string now stand away from the surface of the earth? Explain your reasoning.

EASY 10pts. for whoever shows work and some explanation!!!

THANKS

Answer 1

Circumference = 2 * pi * r

Therefore, Radius = Circumference / 2 / pi

Circumference increases by 15 ft

So, Radius increases by ('stand away') 15 / 2 / pi = 2.387 ft

Long-hand Version:

Circumference = 2 * pi * r

Radius of Earth = 7926 / 2 = 3963 miles

Circumference = 24,900.26337 miles

5280 ft = 1 mile, therefore 15 ft = 15 / 5280 = 0.00284 miles

Circumference (longer string) = 24,900.26337 + 0.00284

= 24,900.26621 miles

Radius = Circumference / 2 / pi

Radius (longer string) = 24,900.26621 / 2 / pi

= 3963.000452 miles

'Stand away' = Radius (longer string) - Radius

= 3963.000452 - 3963

= 0.000452 miles

or 0.000452 * 5280 = 2.387 ft

Answer 2

Relavent equation: circumference = 2 * pi * radius

Step 1:Figure out the circumference of the earth.

Step 2:Add the extra 15ft to that.

Step 3: Calculate the radius of the circle formed by the longer string.

Step 4: Figure out how much more it is than the radius of the earth.

Answer 3

I don't think you have the right answer yet. These solutions don't use the same units consistently. If you give the change in length in feet, then you should state the circumference in feet, not miles.

Intuitively, I think the difference would be much smaller than these answers give.