11-3 Arc Length, Sectors & Sections.ppt
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This document contains examples of calculating arc lengths, sector areas, and section areas of circles. It demonstrates how to find the arc length or sector area as a fraction of the total circumference or total area of the circle based on the central angle. It also shows how to calculate the area of a section by subtracting the area of a triangle from the area of the corresponding sector. Key formulas used include the circumference formula C=2Ï€r, the area formula for a circle A=Ï€r^2, and the area formula for a triangle A=1/2bh.
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11-3 Arc Length, Sectors & Sections.ppt
- 1. Jim Smith JCHS Arc Length, Sectors, Sections spi.3.2.B spi.3.2.L
- 2. 7 C = 2Ï€r C = 2Ï€7 C = 14Ï€
- 3. 9 A = πr² A = π9² A = 81π
- 4. A B The length of AB represents a fractional part of the circle’s circumference. If the mAB Is 90°, then the length of AB is 90/360th (1/4th) of the circumference.
- 5. A B 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 AB = 8π 3
- 7. X Y Z 120° Find the length of XYZ 9 XYZ = 240 of 18π 360 XYZ = 2 · 18π 3 1 XYZ = 12π 360° - 120° 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 360
- 10. 60° 60 of circle’s area 360 12 Area = πr² A = 144π Sector area = A = 1 of 144π 6 144π = 24π 6
- 12. AREA OF SECTION = AREA OF SECTOR – AREA OF TRIANGLE ¼ π r² - ½ bh
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