In the given figure, two concentric circles with centre O have radii 14 cms and 7 cms. If $\angle AOB = 30^{\circ}$, find the area of the shaded region.

The shaded region is the ring (area between the two circles) excluding the $30°$ sector between radii OA and OB.

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Area of the ring $= \pi R^2 - \pi r^2$

$= \pi(R^2 - r^2)$

$= \pi(14^2 - 7^2)$

$= \pi(196 - 49)$

$= 147\pi$

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The unshaded part is the $30°$ sector of the ring, so the shaded part spans $360° - 30° = 330°$ of the ring.

Shaded Area $= \dfrac{330°}{360°} \times 147\pi$

$= \dfrac{11}{12} \times 147\pi$

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Using $\pi = \dfrac{22}{7}$:

$= \dfrac{11}{12} \times 147 \times \dfrac{22}{7}$

$= \dfrac{11}{12} \times 21 \times 22$

$= \dfrac{11}{12} \times 462$

$= \dfrac{5082}{12}$

$= 423.5$ sq. cms