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

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

                    

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The area of shaded region can be easily found by using formula of area of sector.

Area of shaded region is given by  :    Area of sector  OAFC   -   Area of sector OBED

                                                         =\ \frac{40^{\circ}}{360^{\circ}}\times \pi (14)^2\ -\ \frac{40^{\circ}}{360^{\circ}}\times \pi (7)^2

                                                         =\ \frac{616}{9}\ -\ \frac{154}{9}\ =\ \frac{462}{9}

                                                         =\ 51.33\ cm^2 

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