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11.6: Area of circles, sectors, and segments

11.6: Area of circles, sectors, and segments. Area of a circle. A circle = r = radius C = 2 π r r = radius, C = circumference. Example 1. Find the circumference of a circle with area 100 π cm 2 . Sectors. Def: A sector of a circle is a region that is bounded by two radii and an arc

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11.6: Area of circles, sectors, and segments

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  1. 11.6: Area of circles, sectors, and segments

  2. Area of a circle • Acircle = • r = radius • C = 2πr • r = radius, C = circumference

  3. Example 1 • Find the circumference of a circle with area 100π cm2 .

  4. Sectors • Def: A sector of a circle is a region that is bounded by two radii and an arc • Asector = • r = radius • m = measure of intercept arc The sector is the shaded area of this circle.

  5. Example 2 • Find the area of the sector. 30˚ 8

  6. Example 3 • Find the area of the sector. 3 225˚

  7. Example 4 • Find the area of the sector. 12

  8. Example 5 • Find the area of the following shape. 16 20

  9. Segments of a circle • Def: A segment of a circle is the region bounded by a chord and its corresponding arc The shaded region of this circle is a segment.

  10. Finding the area of a segment • Draw a triangle with the endpoints of the chord and the center of the circle as vertices. • Find the area of the sector created. • Find the area of the triangle created. • Subtract: Asector - Atriangle

  11. Example 6 Given: radius of ʘO = 4 Find: the area of segment AB A 90˚ O B

  12. Example 7 Given: CD = 3 Find: the area of segment CD D 60˚ C

  13. Example 8 Given: radius of ʘO = 8 Find: area of sector EF E 120˚ F

  14. Example 9 • Find the area of the shaded region. 6 2

  15. Homework p. 539 1b, 5a-d, 6, 7, 9a-b, 10, 11a,b, 12, 14a

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