SOLUTION: Suppose that the surface of the earth is smooth and spherical and that the distance around the equator is 25,000 miles. A steel band is made to fit snugly around the earth at the e

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Question 31480: Suppose that the surface of the earth is smooth and spherical and that the distance around the equator is 25,000 miles. A steel band is made to fit snugly around the earth at the equator, then the band is cut and a piece of band 18 feet long is inserted. What will the gap be, all the way around, between the band and the earth's surface? (Round to three decimal places) (One mile=5280 feet) ((Please explain your work and answer at an algebra 2 level! Thanks again! :-P ))
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is really asking:
What is the difference in the radii of two circles, one having a circumference (C1) of 25,000 miles and the other having a circumference (C2) of 25,000 miles + 18 feet.
The circumference (C) of a circle, in terms of the radius (r), is given by:
C+=+2%28pi%29r Rewrite this in terms of r.
r+=+C%2F2%28pi%29
For the first circumference (C1=25,000 miles), we can write:
r1+=+C1%2F2%28pi%29
For the expanded circumference (C2=25,000 mi + 18 ft) we can write:
r2+=+C2%2F2%28pi%29
To find the difference (d), we'll subtract r1 from r2.
d+=+C2%2F2%28pi%29+-+C1%2F2%28pi%29
d+=+%28C2-C1%29%2F2%28pi%29
But C2-C1+=+18feet
So:
d+=+18%2F2%28pi%29
d+=+9%2F%28pi%29
d+=+2.865Feet.