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CIRCLES

Learn about arc length, sector area, and section area in circles with examples and formulas. Discover how to calculate the length of arcs, the area of sectors, and the area of sections.

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CIRCLES

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

  2. Circumference C = 2πr C = 2π7 C = 14π 7

  3. area A = πr² A = π9² A = 81π 9

  4. A B ARC LENGTH 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 Find the length of AB C = 2 π r C = 2 π 6 C = 12π 6 90/360 = ¼ Length of AB = ¼·12π = 3π

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

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

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

  9. Find the shaded area A = πr² A = 64π 8 Sector area = ¼ of 64π 64π = 16π 4 90 of circle’s area 360

  10. Sector area = A = 1 of 144π 6 144π = 24π 6 60° Area = πr² A = 144π 12 60 of circle’s area 360

  11. Sections Let’s talk pizza

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

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

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