jmc

The area that is not watered is the area inside the square but outside the circle. The area of the square is $500\cdot 500=250000$ square meters. To find the area of the circle, we note that the diameter of the circle is equal to a side of the square, so the radius is $500/2=250$ meters. Thus, the area of the circle is $\pi 250^2\approx 196300$ square meters. Thus, the unwatered region has area $250000-196300\approx \boxed{54000}$ square meters.