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$The circle has center O, and the central angle of the shaded sector measures 180^(@). The area of the shaded sector is what fraction of the area of the circle?$

The circle has center $O$ , and the central angle of the shaded sector measures $180^{\circ}$ . The area of the shaded sector is what fraction of the area of the circle?

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Q. The circle has center

O

, and the central angle of the shaded sector measures

180^{\circ}

. The area of the shaded sector is what fraction of the area of the circle?

Central Angle Explanation: The central angle of the shaded sector is $180$ degrees, which is half of the $360$ degrees in a full circle. This means that the shaded sector is half of the circle.
Fraction Comparison: To find the fraction of the area of the shaded sector compared to the whole circle, we can set up a ratio of the central angles. Since the central angle of the shaded sector is $180$ degrees out of the $360$ degrees of the whole circle, the fraction is $\frac{180}{360}$ .
Fraction Simplification: Simplify the fraction $\frac{180}{360}$ by dividing both the numerator and the denominator by $180$ .
Final Area Comparison: After simplifying, we get $\frac{180}{360} = \frac{1}{2}$ . Therefore, the area of the shaded sector is $\frac{1}{2}$ of the area of the entire circle.