We are given a circle with center C. The radius of the circle is 5 inches. The angle ACB is 36 degrees. We need to find the area of the shaded sector.

1. Problem Description

We are given a circle with center C. The radius of the circle is 5 inches. The angle ACB is 36 degrees. We need to find the area of the shaded sector.

2. Solution Steps

The formula for the area of a sector of a circle is:

$Area = \frac{\theta}{360} * \pi r^2$

where $\theta$ is the central angle in degrees, and $r$ is the radius of the circle.

In our case, $\theta = 36^{\circ}$ and $r = 5$ inches.

Plugging these values into the formula, we get:

$Area = \frac{36}{360} * \pi (5^2)$

$Area = \frac{1}{10} * \pi (25)$

$Area = \frac{25\pi}{10}$

$Area = \frac{5\pi}{2}$

$Area \approx \frac{5 * 3.14}{2} = \frac{15.7}{2} = 7.85$

The area of the shaded sector is approximately $7.85$ square inches.

3. Final Answer

The area of the shaded sector is approximately 7.9 $in^2$. So the answer is A.