Q.The central angle of a sector of circle of area $9\pi$ sq.cm is $60°$, the perimeter of the sector is
A) $\pi$ B) $3+\pi$ C) $6+\pi$ D) $6$

For a sector of a circle of radius $r$ whose central angle is $\theta$ radians, the sector's area $A$ is directly proportional to $\theta$ (as a fraction of the full circle's area $\pi r^{2}$ corresponding to the full angle $2\pi$):

$\frac{A}{\pi r^{2}} = \frac{\theta}{2\pi} \quad\Longrightarrow\quad A = \frac{1}{2}r^{2}\theta$ …