Question 113212
The border is a circular ring.  The inside radius of the ring is 7 feet, because the diameter of the pool is 14 feet.  Let the width of the border be x, then the outer radius of the walkway ring is x + 7.


If the border was one big circle with no pool in the center, the surface area would be {{{A=pi(x+7)^2}}}.  But we have to subtract the area represented by the pool in the center, and that area is {{{A=pi*7^2}}}.


So the equation for the area of the border is {{{A=pi(x+7)^2-pi*7^2}}}


Now we need to compute the surface area of the border knowing that it is 1 inch thick and consists of a cubic yard of concrete.  First of all, there are 12 X 12 X 12 = 1728 cubic inches in a cubic foot and 27 cubic feet in a cubic yard, so there are 1728 X 27 = 46656 cubic inches in a cubic yard.  The volume of the border is just its surface area times its thickness, so since we know the volume to be 46656 cubic inches, we can divide by 1 inch to get 46656 square inches of area.  But since the radius measurements are in feet, lets convert the square inches back to square feet.  There are 12 X 12 = 144 square inches in a square foot, so there are {{{46656/144=324}}} square feet of area to the border.


Now we are getting somewhere.  We can now write:


{{{pi(x+7)^2-pi*7^2=324}}}
{{{(x+7)^2-7^2=324/pi}}}
{{{x^2+14x+49-49=324/pi}}}
{{{x^2+14x-324/pi=0}}}
{{{x^2+14x-103.185=0}}}


{{{x = (-14 +- sqrt( 14^2-4*(-103.185) ))/(2) }}} 


I'll leave verification of the arithmetic to you, but you will get two solutions:

5.34 and -19.34.  Since we are looking for a length, the negative result is clearly an absurdity, so it can be excluded.  The width of the border is then 5.34 feet.


Hope this helps,
John