Question 150270: Suppose you tie a rope around the earth at the equator (circumference approx. 25,000 miles). Let's say you pull the rope as tight as it will go and then add back 6 feet of slack before tying the knot. If the extra rope is distributed evenly around the globe will there be enough space between the rope and the surface of the earth for a worm to crawl under?
Assume the earth is a perfect sphere and the rope does not stretch.
I have no idea how to approach this problem. Can anyone help?
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! The essential idea here is comparing the radii of two circles, one whose circumference is 25,000 miles and the othe whose circumference is 25,000 miles + 6 feet.
So, let's find the radius of the first circle (the earth at the equator).
As you know, the circumference of a circle is given by:
Where D is the diameter. In terms of the radius, R, you can substitute D = 2R, so...
Solving for the radius, you get:

Now we need to convert the circumference, C, of 25,000 miles to feet, so (25,000 mi)*(5280 ft/mi) = 132,000,000 ft. Now we can find the radius of the idealized earth in feet.
Substitute C = 132,000,000 ft. and Approx.

Ft.
Now we'll add 6 ft. to the circumference and find the new radius.
Substitute C = 132,000,006 and Approx.

Ft.
Now, to find out how much room there is between the first radius and the second radius, we'll subtract the two.
= feet. This would be the difference between the two radii and thus the amount of room between the earth and the expanded rope belt around the equator.
I would have to conclude that this is sufficient room for a worm to crawl under, unless of course, the worm is very very fat!
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