To find the area of a sector of a circle, you 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:
- \( r = 6 \) inches,
- \( \theta = 120^\circ \).
Now plug in the values:
\[ A = \frac{120}{360} \times \pi \times (6)^2 \]
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]
Then the equation becomes:
\[ A = \frac{120}{360} \times \pi \times 36 \]
Simplifying \( \frac{120}{360} \):
\[ \frac{120}{360} = \frac{1}{3} \]
Now substituting that back into the equation:
\[ A = \frac{1}{3} \times \pi \times 36 \]
This simplifies to:
\[ A = 12\pi \]
Thus, the area of the sector is:
\[ A = 12\pi \text{ in}^2 \]
So the correct response is:
A=12π in.²
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