Find the area of the shaded region in the figure,if the radii of the two concentric circles with center $O$ are $7\, cm$ and $14\, cm$ respectively and $\angle AOC = 40^{\circ}$. [Use $\pi = \frac{22}{7}$]

(N/A) The shaded region is the area of the sector of the larger circle minus the area of the sector of the smaller circle.
Let $R = 14\, cm$ be the radius of the larger circle and $r = 7\, cm$ be the radius of the smaller circle.
The central angle $\theta = 40^{\circ}$.
The area of a sector is given by the formula $\frac{\theta}{360^{\circ}} \times \pi r^2$.
Area of the shaded region = Area of sector $OAC$ - Area of sector $OBD$
$= \frac{40^{\circ}}{360^{\circ}} \times \pi R^2 - \frac{40^{\circ}}{360^{\circ}} \times \pi r^2$
$= \frac{1}{9} \times \pi (R^2 - r^2)$
$= \frac{1}{9} \times \frac{22}{7} \times (14^2 - 7^2)$
$= \frac{1}{9} \times \frac{22}{7} \times (196 - 49)$
$= \frac{1}{9} \times \frac{22}{7} \times 147$
$= \frac{1}{9} \times 22 \times 21$
$= \frac{462}{9} = \frac{154}{3} \approx 51.33\, cm^2$.