Answer:
D). [tex] \frac{3}{2} \pi\: units^2 [/tex]
Explanation:
Let the [tex] m\angle BOC = x\degree [/tex]
[tex] \therefore m\angle AOB = 2x\degree[/tex]
[tex] \because m\angle AOB+m\angle BOC = 180\degree\\..(straight \: line \: \angle 's) \\
\therefore 2x + x = 180\degree \\
\therefore 3x = 180\degree \\\\
\therefore x = \frac{180\degree}{3}\\\\
\therefore x = 60\degree \\
\therefore 2x= 2\times 60\degree = 120\degree \\
\implies m\angle BOC = 60\degree \\
\therefore central \: \angle \: (\theta) = 60\degree \\
Radius\: of \:circle \: (r) = 3\: units \\\\
Area \: of\: shaded \: region\\\\ = \frac{\theta}{360\degree}\times \pi r^2 \\\\
= \frac{60\degree}{360\degree}\times \pi \times 3^2 \\\\
= \frac{1 }{6}\times \pi \times 9 \\\\
= \frac{1 }{2}\times \pi \times 3 \\\\
\huge \purple {\boxed {= \frac{3}{2} \pi\: units^2}} \\\\
[/tex]
