Question

the circle has center o, and the central angle of the shaded sector measures 60°. 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 $\frac{1}{12}$ b $\frac{1}{10}$ c $\frac{1}{8}$ d 1

Explanation:

Step1: Recall sector - circle area relation

The fraction is $\frac{\text{central angle of sector}}{\text{total degrees in circle}}$.

Step2: Calculate the fraction

$\frac{60}{360}=\frac{1}{6}$ (but this is not in options, likely a mis - type in problem setup as the correct method is this). If we assume we want to simplify from the given approach, the correct fraction of the area of the shaded sector to the area of the circle is $\frac{60}{360}=\frac{1}{6}$. Since the closest correct - looking option based on the method is not present, if we assume a wrong - options scenario and go by the principle of dividing the sector angle by total circle angle, the answer should be $\frac{1}{6}$. But among the given options, if we consider the ratio calculation conceptually, we divide the angle of the sector by the total angle of the circle.

Answer:

There is no correct option among A. $\frac{1}{12}$, B. $\frac{1}{10}$, C. $\frac{1}{8}$, D. $1$. The correct answer should be $\frac{1}{6}$.