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Question -

Find the area of theshaded region in Fig. 12.20, if radii of the two concentric circles with centreO are 7 cm and 14 cm respectively and AOC = 40┬░.



Answer -

Given,

Angle made by sector = 40┬░,

Radius the inner circle = r = 7 cm, and

Radius of the outer circle = R = 14 cm

We know,

Area of the sector = (╬╕/360┬░)├Ч╧Аr2

So, Area of OAC = (40┬░/360┬░)├Ч╧Аr2┬аcm2

= 68.44 cm2

Area of the sector OBD = (40┬░/360┬░)├Ч╧Аr2┬аcm2

= (1/9)├Ч(22/7)├Ч72┬а= 17.11 cm2

Now, area of the shaded region ABDC = Area ofOAC тАУ Area of the OBD

= 68.44 cm2┬атАУ 17.11 cm2┬а=51.33 cm2

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