To find the area of a sector of a circle, you can use the following formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
Where:
- \( A \) is the area of the sector,
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle.
Given \( \theta = 115^\circ \) and \( r = 6 \) cm, we can substitute these values into the formula:
\[ A = \frac{115}{360} \times \pi \times (6)^2 \] \[ A = \frac{115}{360} \times \pi \times 36 \] \[ A = \frac{115 \times 36}{360} \times \pi \] \[ A = \frac{4140}{360} \times \pi \] \[ A = 11.5 \times \pi \]
Now, calculating \( 11.5 \times \pi \):
Using \( \pi \approx 3.14 \) for estimation:
\[ A \approx 11.5 \times 3.14 \approx 36.13 \text{ cm}^2 \]
So, the area of the sector is:
\[ A \approx 36.13 \text{ cm}^2 \]
Thus, the correct response is:
A = 36.13 cm².