Question

If O is the center of the circle above, what fraction of the circular region is shaded?

• A. $\frac{1}{12}$
• B. $\frac{1}{9}$
• C. $\frac{1}{6}$
• D. $\frac{1}{4}$
• E. $\frac{1}{3}$

Answer 1

The correct option is C $\frac{1}{6}$

We know that the angle of the top unshaded part is $150$ degrees, so we can also conclude that the angle of the bottom unshaded part is also $150$ degrees.

So, a total of $300$ degrees is unshaded.

Since there are $360$ degrees in the entire circle, we can see that $60$ degrees is shaded.

Therefore, we have

$\frac{60}{360}=\frac{1}{6}$

Hence, $\frac{1}{6}$ of the circlular region is shaded.