Answer: C.
![17.3\ in^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zgzyds9nz6aixk8uw6ebb1mjx5quermbpg.png)
Explanation:
The area of a sector with central angle x and radius r is given by :-
![A=(x)/(360^(\circ))*\pi r^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6m30psao9jum1l1npt4kfhgl16o633dt24.png)
In the given picture, the radius of the circle = 3.7 in.
The central angle =
![145^(\circ)](https://img.qammunity.org/2020/formulas/mathematics/high-school/95iamf5rw9lndsvuf0ijiv6yub1np3akuc.png)
Now, the area of the sector in the picture will be :-
![A=(145^(\circ))/(360^(circ))*\pi (3.7)^2\approx 17.3\ in^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/27kwu34g0lgjq3s9bzkgl9tt4el9meqf9o.png)
Hence, the approximate area of the shaded sector in the circle =
![17.3\ in^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zgzyds9nz6aixk8uw6ebb1mjx5quermbpg.png)