Uniform width means that it is the same width all around the pool, so the

inner and outer edges constitute two concentric circles.

If the width of the border is , the the area of the border is:

That is it is the difference of area between the circle of radius and one of radius .

Then the volume of cement required is:

as ,

so. as we have:

rearranging this gives:

.

This is a quadratic in which can be solved using the quadratic formula to give:

or:

The second of these is negative and so cannot be the solution which leaves the first, so:

RonL