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

Asked by Pragya Singh | 1 year ago |  163

##### Solution :-

Radius of the larger circle, R = 21 cm

Radius of the smaller circle, r = 7 cm

Angle made by sectors of both concentric circles = 30°

Area of the larger sector = $$\dfrac{30°}{360°}$$×πRcm2

= $$\dfrac{1}{12}\times \dfrac{22}{7}×21^2$$ cm2

= $$\dfrac{231}{2}$$cm2

Area of the smaller circle = ($$\dfrac{30°}{360°}$$)×πrcm2

= $$\dfrac{1}{12}\times \dfrac{22}{7}×7^2$$ cm2

=$$\dfrac{77}{6}$$ cm2

Area of the shaded region = ($$\dfrac{231}{2}$$) – ($$\dfrac{77}{6}$$) cm2

$$\dfrac{616}{6}$$ cm2 = $$\dfrac{308}{3}$$cm2

Answered by Abhisek | 1 year ago

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