Q.20 meter of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 meters, then the maximum area (in sq. m.) of the flower-bed is
A) 15 B) 20 C) 25 D) 30

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 $2\pi$):

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