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Unit 6 Ch. 10.2, 11.4 and 11.5

Unit 6 Ch. 10.2, 11.4 and 11.5. Warm up Homework check Notes – Central Angles and Arcs Circumference and Arc Length Areas of Circles and Sectors. 127° 60° 83° 173° 34° 136° 83° 107° 24 A. 270° B. 27 min C. 37 min D 100°.

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Unit 6 Ch. 10.2, 11.4 and 11.5

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  1. Unit 6 Ch. 10.2, 11.4 and 11.5 • Warm up • Homework check • Notes – Central Angles and Arcs Circumference and Arc Length Areas of Circles and Sectors

  2. 127° • 60° • 83° • 173° • 34° • 136° • 83° • 107° • 24 A. 270° • B. 27 min • C. 37 min • D 100° Homework 10.2 Central Angles • 80° • 165° • 258° • 195° • 80° • 110° • 90° • 70° • 57° • 57°

  3. 10.2 Central angles and arcs • An angle whose vertex is at the center of the circle and is formed by two radii. • The intercepted arc has the same measure as the central angle R Major arc

  4. 11.4: Circumference and Arc Length

  5. The circumference of a circle is ___________ or ___________, where d is the diameter of the circle and r is the radius of the circle.

  6. Example 1 So we need to find the circumference and then multiply times 15. First we will need the radius or diameter. d = 5.5+15+5.5 =26in Second find the Circumference Last multiply the Circumference times 15. Distance = 15*81.68 =1225.2 inches about 102 feet

  7. Arc length • An ____________ is a portion of the circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units).

  8. Example 2

  9. Example 3

  10. Try these on your own. About 15.71 in, about 5.41 ft About 68 revolutions About 81.68 m About 4.01 ft About 5.89 yds

  11. 11.5: Areas of Circles and Sectors

  12. Formulas: Area of a Circle: Area of a Sector:

  13. Example 1

  14. Example 2

  15. Example 3

  16. 20(28) – 122 – = area to paint 560 – 144 – = area to paint Example 4 Area of rectangle – area of square – area of semicircle = area of wall to paint 359.45 ≈ area to paint So the answer is C. 359 ft2

  17. Try these on your own. 196 or about 615.75 sq ft About 205.25 sq ft About 410.50 sq ft About 907.92 sq cm About 43.74 sq m

  18. Geometry homework WS 11.4-11.5

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