1. Jim Smith JCHS Arc Length, Sectors, Sections spi.3.2.Bspi.3.2.L

2. 7 C = 2πr C = 2π7 C = 14π

3. 9 A = πr² A = π9² A = 81π

4. AB The length of AB represents a fractional part of the circle’s circumference. If the mAB Is 90°, then the length of AB is 90/360 th (1/4 th ) of the circumference.

5. AB 6 Find the length of AB C = 2 π r C = 2 π 6 C = 12π Length of AB = ¼ ·12π = 3π 90/360 = ¼

6. A B 60° 8 C = 2πr C = 16π AB = 60/360 of 16π AB = 1/6 · 16π AB = 1 · 16π 6 1 6 1 AB = 8π 3

7. X YZ120° Find the length of XYZ XYZ 9 XYZ = 240 of 18π 360 360 XYZ = 2 · 18π 3 1 3 1 XYZ = 12π 360° 360° - 120° 240° 240° C = 2πr C = 18π

8. Sectors are a fractional part of a circle’s area

9. Find the shaded area 8 A = πr² A = 64π Sector area = ¼ of 64π 64π = 16π 4 90 of circle’s area 90 of circle’s area360

10. 60° 60 of circle’s area 60 of circle’s area360 12 Area = πr² A = 144π Sector area = A = 1 of 144π 6 144π = 24π 6

11. Sections Let’s talk pizza

12. AREA OF SECTION = AREA OF SECTOR – AREA OF TRIANGLE AREA OF SECTOR – AREA OF TRIANGLE ¼ π r² - ½ bh ¼ π r² - ½ bh

13. Area of section = area of sector – area of triangle area of sector – area of triangle ¼ π r² - ½ bh ¼ π r² - ½ bh 10 A OF = ½∙10∙10= 50 50 A OF SECTION = 25π - 50 A of circle = 100π A OF = ¼ 100π = 25π 25π