Answer: The answer is [tex]A_o=2\pi\sqrt{\dfrac{7}{22}(25x^2-12x-9)}.[/tex]
Step-by-step explanation: Given that the area of the whole circle is represented by the expression
[tex]A_c=25x^2-12x-9.[/tex]
We are to find the area of the outer ring of the circle, i.e., to find the circumference of the circle.
Now, if 'r' represents the radius of the circle, then we have
[tex]A_c=\pi r^2\\\\\Rightarrow \dfrac{22}{7}r^2=25x^2-12x-9\\\\ \Rightarrow r^2=\dfrac{7}{22}(25x^2-12x-9)\\\\\Rightarrow r=\sqrt{\dfrac{7}{22}(25x^2-12x-9)}.[/tex]
Thus, the area of the outer ring is
[tex]A_o=2\pi r=2\pi\sqrt{\dfrac{7}{22}(25x^2-12x-9)}.[/tex]
