To find the area of a sector of a circle, you can use the formula:
\[ \text{Area of the sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.
Given:
- \(\theta = 168^\circ\)
- \(r = 15\) inches
Now, substitute these values into the formula:
\[ \text{Area of the sector} = \frac{168}{360} \times \pi \times (15)^2 \]
First, calculate \(15^2\):
\[ 15^2 = 225 \]
Now plug that into the formula:
\[ \text{Area of the sector} = \frac{168}{360} \times \pi \times 225 \]
Calculating \(\frac{168}{360}\):
\[ \frac{168}{360} = \frac{14}{30} = \frac{7}{15} \]
Now, substitute this back into the equation:
\[ \text{Area of the sector} = \frac{7}{15} \times \pi \times 225 \]
Next, calculate \(\frac{7}{15} \times 225\):
\[ \frac{7 \times 225}{15} = \frac{1575}{15} = 105 \]
Therefore, the area of the sector is:
\[ \text{Area of the sector} = 105\pi \text{ square inches} \]
If you would like a numerical approximation, using \(\pi \approx 3.14\):
\[ 105\pi \approx 105 \times 3.14 \approx 329.7 \text{ square inches} \]
Thus, the area of the sector of the circle is \(105\pi\) square inches, or approximately \(329.7\) square inches.