Question

In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If $\angle POQ={30}^{\circ }$, find the area of the shaded region.

Answer 1

∠AOB = 30°
Smaller Radius OC (r) = 7 cm
Bigger Radius OB(R)= 3.5cm
Angle made by sectors of both concentric circles $\theta ={30}^{\circ }$

$AreaofthelargersectorAOB=\frac{{30}^{\circ }}{{360}^{\circ }}\times \pi R^2{cm}^2$ \

= $\frac{1}{12}\times \frac{22}{7}\times 7^2$

= $12.83{cm}^2$

Area of the smaller sector COD=\frac {30^\circ}{360^\circ} \times \pi{r}^{2} {cm}^{2} \)

= $\frac{1}{12}\times \frac{22}{7}\times (3.5{)}^2{cm}^2$

= $3.20{cm}^2$


Area of shaded region= area of sector AOB - area of sector COD

Area of the shaded region = $69.621{cm}^2$