AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig.). If ∠AOB = 30°, find the area of the shaded region

We know that,  formula for the area of the sector of a circle

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

Where , $\theta$ = angle = 30⁰

r = radius

Thus, we get 

Area of the shaded region = Area of sector ABO - Area of sector CDO

Radius of the sector ABO, r = OB = 21 cm

Area of the sector ABO = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

= $\frac{{30}^0}{{360}^0}$$\times$ ${\mathrm{\pi r}}^2$

Radius of the sector CDO, R = OD = 7 cm

Area of sector CDO = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

= $\frac{{30}^0}{{360}^0}$ $\times$ $\mathrm{\pi }$R²

Area of shaded region = Area of sector ABO - Area of sector CDO

= θ/360° $\times$${\mathrm{\pi r}}^2$ - θ/360° $\times$$\mathrm{\pi }$R²

= θ/360°$\times$ π (r² - R²)

= 30°/360° $\times$ 22/7 [(21)² - (7)²]

= 1/12 $\times$ 22/7$\times$ (441 - 49 )

= 11/42 × 392$\times$

= 308/3 cm²