Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and \(\angle AOC = 40°\)

 

Asked by Pragya Singh | 1 year ago |  101

1 Answer

Solution :-

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 = (\(\dfrac{ θ}{360°} \))×πr2

So, Area of OAC = (\( \dfrac{ 40°}{360°} \))×πrcm2

= 68.44 cm2

Area of the sector OBD = (\( \dfrac{ 40°}{360°} \))×πrcm2

= (\( \dfrac{1}{9}\))×(\( \dfrac{22}{7}\))×7= 17.11 cm2

Now, area of the shaded region ABDC = Area of OAC – Area of the OBD

= 68.44 cm2 – 17.11 cm= 51.33 cm2

Answered by Abhisek | 1 year ago

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