Ex 12.3, 2 - Find area, if radii of two concentric circles - Ex 12.3

Ex 12.3, 2 - Chapter 12 Class 10 Areas related to Circles - Part 2
Ex 12.3, 2 - Chapter 12 Class 10 Areas related to Circles - Part 3

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Transcript

Question 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.