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Question

Find the area of the shaded region (in cm2) as shown in figure of the two concentric circles with centre O and radius 7 cm and 14 cm respectively. Given ∠AOC = 40∘. (use π = 227)

A

42.1 cm2

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B

51.32 cm2

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C

67.8 cm2

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D

96.5 cm2

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Solution

The correct option is B 51.32 cm2 Given: radius for sector OAC = 14 cm and angle subtended = 40∘ and radius for sector OBD = 7 cm and angle subtended = 40∘ Area of Sector = x∘360∘×πr2 Required area = [Area of sector OAC – Area of sector OBD] =40360×227×142–40360×227×72 = 68.42 - 17.1 = 51.32 cm2 ∴ Area of shaded region = 51.32 cm2

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