In Figure , two concentric circles with centre O, have radii 21 cm and 42 cm. Ifangle AOB = 60 degreeNow, find the area of the shaded region. [Use = 22/7 ]

Answer :

We know Area of sector of circle  = $\frac{\theta }{360°}\times {\mathrm{\pi r}}^2$
And

Area of shaded region  =  Area of sector with radius( OA = 42 )  - Area of sector with radius ( OC = 21 )

So,

Area of shaded region  =  $\frac{60°}{360°}\times \frac{22}{7} \times 42\times 42 - \frac{60°}{360°}\times \frac{22}{7} \times 21\times 21$

Area of shaded region  =  $\frac{1}{6}\times \frac{22}{7} \times 42\times 42 - \frac{1}{6}\times \frac{22}{7} \times 21\times 21$

Area of shaded region  =  $22\times 42 - 11\times 21$

Area of shaded region  =  924  - 231

Area of shaded region  =  693 cm²                                                      ( Ans )