Question

A 25,000-mile steel band is placed around the earth, snugly fit at the equator. The band is cut, and 36 inches of string is spliced into the steel band. This new, larger circular band is placed around the earth, so its center coincides with the center of the earth, and a gap is created. How wide is this gap?

When you have finished, post your work showing the formula used for calculating the gap (g), show all calculations solving for g (gap), and a statement interpreting the results of your work.

Answer 1

Answer: 2.865Feet.

Step-by-step explanation: 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×π29r Rewrite this in terms of r.

r=C/2×π

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.