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.

AB and CD are respectively arcs of two concentric circles of radii 21 cm  and 7 cm - CBSE Class 10 Maths - Learn CBSE Forum

Asked by Pragya Singh | 1 year ago |  163

1 Answer

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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