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

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Solution

Radius of inner circle = 7 cm

Radius of outer circle = 14 cm

Area of shaded region = Area of sector OAFC − Area of sector OBED

$= \frac{40 °}{360 °} \times π (14)^{2} - \frac{40 °}{360 °} \times π (7)^{2} = \frac{1}{9} \times \frac{22}{7} \times 14 \times 14 - \frac{1}{9} \times \frac{22}{7} \times 7 \times 7 = \frac{616}{9} - \frac{154}{9} = \frac{462}{9} = \frac{154}{3} {cm}^{2}$

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