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

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

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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 = (30°/360°) × πRcm2

= (1/12) × (22/7) × 21cm2

= 231/2cm2

Area of the smaller circle = (30°/360°) × πrcm2

= 1/12 × 22/7 × 7cm2

=77/6 cm2

Area of the shaded region = (231/2) – (77/6) cm2

= 616/6 cm2 

= 308/3cm2

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