Answer:
The area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]
Explanation:
Given the figure in the attached image.
The area of the shaded region is the area of the larger circle minus the area of the smaller circle;
[tex]\begin{gathered} A=\frac{\pi D^2}{4}-\frac{\pi d^2}{4} \\ A=\frac{\pi}{4}(D^2-d^2) \end{gathered}[/tex]
Given;
[tex]\begin{gathered} D=6 \\ d=3\frac{1}{2} \end{gathered}[/tex]
Substituting the given values;
[tex]\begin{gathered} A=\frac{\pi}{4}(D^2-d^2) \\ A=\frac{\pi}{4}(6^2-3.5^2) \\ A=\frac{\pi}{4}(23.75) \\ A=18.65\text{ }in^2 \\ A=18.7\text{ }in^2 \end{gathered}[/tex]
Therefore, the area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]
