Geometry & Mensuration
Aptitude

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Q.

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

Image for Mensuration, Aptitude:2175-1

 A.

\(\dfrac{1}{12}\)

 B.

\(\dfrac{1}{9}\)

 C.

\(\dfrac{1}{6}\)

 D.

\(\dfrac{1}{3}\)

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Solution:
Option(C) is correct

Vertical angles are congruent, so \(150^\circ+150^\circ = 300^\circ\) of the circle is not shaded.

Since there are \(360^\circ\) in a circle, this makes

\(360^\circ - 300^\circ = 60^\circ\) of the circle shaded.

The fraction of the circular region that is shaded is thus 

\(=\dfrac{60}{360}\)

\(=\dfrac{1}{6}\)


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