Q18 of 46 Page 1

In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. Of , then find the area of the shaded region.

To find the area of the shaded region, we need to find the area of the whole region and subtract it to the area of the piece of circle OAB.

Area of POQ is given by


Area(POQ) =


⇒ Area(POQ) = [∵, radius (r) of POQ = 7 cm]


⇒ Area(POQ) = …(i)


Area of AOB is given by


Area(AOB) =


⇒ Area(AOB) = [∵, radius (r) of AOB = 3.5 cm]


⇒ Area(AOB) = …(ii)


Area of shaded region is given by


Area = Area(POQ) – Area(AOB)


⇒ Area =


⇒ Area =


⇒ Area =


⇒ Area = 9.625 cm2


Hence, the area of the shaded region is 9.625 cm2.


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