Answer
$r(x)=\frac{x^2(4-\pi)}{4}$
Work Step by Step
The area of the square is $s(x)=x^2$
The area of the circle is $A=\pi r^2$
The difference of the area of the square and the area of the circle is $s(x)-c(x)\\=x^2-\frac{\pi x^2}{4}\\=\frac{4x^2-\pi x^2}{4}\\=\frac{x^2(4-\pi)}{4}\\=r(x)$