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.

Given:

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


= cm2


Similarly, Area of S2 = × × 3.5 × 3.5


= cm2


Thus, using (i), we have


Area of shaded region = -


=


= = cm2


Hence, the area of shaded region is cm2.


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