Question 150270
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:
{{{C = pi*D}}} Where D is the diameter.  In terms of the radius, R, you can substitute D = 2R, so...
{{{C = 2*pi*R}}} Solving for the radius, you get:
{{{R = C/(2*pi)}}}
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.
{{{R[1] = C[1]/(2*pi)}}} Substitute C = 132,000,000 ft. and {{{pi = 3.14}}}Approx.
{{{R[1] = 132000000/(2(3.14))}}}
{{{R[1] = 21019108.28}}}Ft.
Now we'll add 6 ft. to the circumference and find the new radius.
{{{R[2] = C[2]/(2*pi)}}} Substitute C = 132,000,006 and {{{pi = 3.14}}}Approx.
{{{R[2] = 132000006/2(3.14)}}}
{{{R[2] = 21019109.24 }}}Ft.
Now, to find out how much room there is between the first radius and the second radius, we'll subtract the two.
{{{R[2]-R[1] = 21019109.24 - 21019108.28}}} = {{{highlight(0.96)}}}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!