It is given that,
[tex]\begin{gathered} Area\text{ of the shaded region = 260}\pi\text{ cm}^2 \\ Radius\text{ of inner circle = x cm} \\ Radius\text{ of outer circle = 18 cm} \end{gathered}[/tex]
The area of the inner circle is calculated as,
[tex]Area\text{ of inner circle = }\pi x^2[/tex]
The area of the outer circle is calculated as,
[tex]Area\text{ of outer circle = }\pi\times18^2[/tex]
The area of the shaded region is calculated as,
Area of shaded region = Area of the outer circle - Area of the inner circle
[tex]\begin{gathered} Area\text{ of the shaded region = }\pi\times18^2\text{ - }\pi\times x^2 \\ Area\text{ of the shaded region = }\pi\times(18^2-x^2) \\ 260\times\pi\text{ = }\pi\times(18^2-x^2) \\ \end{gathered}[/tex]
The radius of inner circle is calculated as,
[tex]\begin{gathered} 260\text{ = 18}^2-x^2 \\ x^2\text{ = 324 - 260} \\ x^2=\text{ 64} \\ x\text{ = 8} \\ \end{gathered}[/tex]
Thus the value of x is 8 cm.
