Question

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 number of degrees of arc in a circle is 360.) choose 1 answer: a $\frac{1}{4}$ b $\frac{1}{3}$ c $\frac{1}{2}$ d $\frac{2}{3}$

Explanation:

Step1: Recall the formula for sector - area ratio

The ratio of the area of a sector to the area of a circle is equal to the ratio of the central - angle of the sector to the total number of degrees in a circle.

Step2: Calculate the ratio

The central angle of the sector is $180^{\circ}$, and the total number of degrees in a circle is $360^{\circ}$. The ratio is $\frac{180}{360}=\frac{1}{2}$.

Answer:

C. $\frac{1}{2}$