Question

the circle has center o, and the central angle of the shaded sector measures 120°. 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 $\frac{1}{3}$ b $\frac{3}{8}$ c $\frac{2}{5}$ d $\frac{5}{12}$

Explanation:

Step1: Recall sector - circle area relationship

The ratio of the area of a sector to the area of the 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 fraction

The central angle of the sector is $120^{\circ}$ and the total number of degrees in a circle is $360^{\circ}$. The fraction is $\frac{120}{360}=\frac{1}{3}$.

Answer:

A. $\frac{1}{3}$