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26/06/2021 1:24 pm
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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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26/06/2021 1:26 pm
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°) × πR2 cm2
= (1/12) × (22/7) × 212 cm2
= 231/2cm2
Area of the smaller circle = (30°/360°) × πr2 cm2
= 1/12 × 22/7 × 72 cm2
=77/6 cm2
Area of the shaded region = (231/2) – (77/6) cm2
= 616/6 cm2
= 308/3cm2