Ex 12.3, 2
Find the area of the shaded region in figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.
Area of shaded region
= Area of sector AOC – Area of sector BOD
Area of sector BOD
In smaller circle, θ = 40° and r = 7 cm
Area of sector BOD = 𝜃/360×𝜋𝑟2
= 40/360×22/7×(7)2
= 1/9×22/7×7×7
= 1/9×22×7
= 154/9 cm2
Area of sector AOC
In larger circle, θ=40° , r = 14 cm
Area of sector AOC = 𝜃/(360°)×𝜋𝑟^2
= 40/360×22/7×(14)2
= 1/9×22/7×14×14
= 1/9×22×2×14
= 616/9 cm2
Now ,
Area of shaded region = Area of sector AOC – Area of sector BOD
= 616/9−154/9
= (616−154)/9
= 462/9
= 154/3 cm2
Hence, area of shaded region = 154/3 cm2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.