Areas of Circles and Sectors

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Areas of Circles and Sectors Lecture for Monday April 11th

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Areas of Circles and Sectors

  1. 1. Sec. 7 – 7 Areas of Circles & Sectors Objective: To find the areas of circles, sectors and segments of circles
  2. 2. Area of a Circle r r A =  r 2 Pi = 3.14 = 22/7 Radius of Circle r
  3. 3. Example1: How much more pizza is in a 12in diameter pizza than in a 10in diameter pizza? A 12 =  r 2 = 6 2  = 36  = 113.1in 2 A 10 =  r 2 =5 2  = 25  = 78.5in 2 36  - 25  = 11  = 34.6in 2
  4. 4. <ul><li>Sector of a Circle –a region bounded by an arc of the circle & the 2 radii to the arc’s endpoints. </li></ul><ul><ul><li>The area of a sector is a fractional part of the area of a circle. </li></ul></ul><ul><ul><li>Named by one of the arc’s endpoints, the center of a circle, and the other arc endpoint. </li></ul></ul><ul><ul><ul><li>Example: Sector CPD of Circle </li></ul></ul></ul>C P D A = mARC 360  r 2 Area of sector Fraction of Circle Area of Circle P
  5. 5. Example 2: Find the area of sector ABS 100  6cm A sector = mAS 360  r 2 = 100/360 • (6 2 )  = .278 • (36  ) = 31.4cm 2 B A S
  6. 6. <ul><li>Segment of a Circle – is part of a circle bounded by an arc & the segment joining its endpoints. </li></ul>
  7. 7. <ul><li>Segment of a Circle </li></ul>Area of a Δ A = ½ bh Area of the Segment A segment = A sector - A Δ
  8. 8. Example 3: Find the area of the segment m  ABC = 90 ° C B A 45 45 A segment = A sector CBA – A Δ CBA = (mCA)360 •  r 2 - ½bh = (90)/360 •  (10) 2 - ½(14.2)(7.1) = 78.5 – 50.4 = 28.1cm 2 10cm 45 = 10/ √2 =7.1
  9. 9. What have we learned?? <ul><li>Area of a Circle </li></ul><ul><li>Area of a Sector of a Circle </li></ul><ul><li>Area of a segment </li></ul>A = mARC 360  r 2 A segment = A sector - A Δ A =  r 2 A =  r 2

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