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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.
Radius of inner circle = 3.5 cm
Radius of outer circle = 7 cm
∠POQ = 30°
Let the sector made by the arcs PQ and AB be S1 and S2 respectively.
Then, Area of shaded region = Area of S1 – Area of S2 ………….(i)
∵ Area of sector = × πr2
∴ Area of S1 = × × 7 × 7
Similarly, Area of S2 = × × 3.5 × 3.5
Thus, using (i), we have
Area of shaded region = -
= = cm2
Hence, the area of shaded region is cm2.