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Question
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see the given figure). If ∠AOB = 30°, find the area of the shaded region. [Use Π = 22/7]
Solution
Area of the shaded region = Area of sector OAEB − Area of sector OCFD
`= 30^@/360^@xxpixx(21)^2 - 30^@/360^@ xx pixx (7)^2`
`=1/12xxpi[(21)^2-(7)^2]`
`=1/12xx22/7xx[(21-7)(21+7)]`
`= (22xx14xx28)/(12xx7)`
`= 308/3 cm^2`
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