To find the area of the sector of a circle, we can use the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(A\) is the area of the sector,
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.
Given:
- \(\theta = 216^\circ\),
- \(r = 7\) inches.
Plugging the values into the formula:
\[ A = \frac{216}{360} \times \pi \times 7^2 \]
Calculating \(7^2\):
\[ 7^2 = 49 \]
Now substitute back in:
\[ A = \frac{216}{360} \times \pi \times 49 \]
Next, simplify \(\frac{216}{360}\):
\[ \frac{216}{360} = \frac{3}{5} \]
Thus, the area becomes:
\[ A = \frac{3}{5} \times \pi \times 49 = \frac{147}{5} \pi \]
Calculating \(\frac{147}{5}\):
\[ \frac{147}{5} = 29.4 \]
So, the area of the sector is:
\[ A = 29.4\pi \]
Therefore, the correct response is:
A = 29.4π in².