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Question
In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
Solution
Area of the shaded portion = Area of sector OPQ − Area of sector OAB
`= 30^circ/360xxpi(7)^2 - 30^circ/360^circxxpi(3.5)^2`
`=22/7xx1/12[(7)^3 - (3.5)^2]`
`= 22/7 xx 1/12[(7)^2-(7/2)^2]`
`=22/7xx1/12xx147/4`
`=77/8 "cm"^2`
Hence, the area of the shaded portion is`77/8` cm2 .
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