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CIRCLES

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  1. CIRCLES Arc Length, Sectors, Sections

  2. Geometry Arc Lengths and Areas of Sectors

  3. Arc Length • The length of part of the circumference. The length of the arc depends on what two things? 1) The measure of the arc. 2) The size of the circle. An arc length measures distance while the measure of an arc is in degrees.

  4. Sector of a circle • A region bounded by 2 radii and an arc. .

  5. Z 120° X Y • Minor Arc • Use 2 letters • Angle is less than or equal to 180 Terminology XZ 9 • Major Arc • Use 3 letters • Angle is greater than 180 C XYZ Central Angle:Any angle whose vertex is the center of the circle m XZ = m<XCZ = 120o The measure of arc XZ equals the measure of angle XCZ

  6. Portions of a Circle: Determine the Arc measure based on the portion given. 180o 120o 90o 60o 90o 180o 120o 60o ¼ ● 360 ½ ● 360 1/3 ● 360 1/6 ● 360

  7. Area of a Sector Formula measure of the central angle or arc m πr2 Area of a sector = 360 The area of the entire circle! The fraction of the circle! .

  8. Arc Length Formula measure of the central angle or arc m The circumference of the entire circle! 2πr Arc Length = 360 The fraction of the circle! .

  9. Find the length of AB and the area of sector AOB. A 300o 120o 108o 240o B 90o B 120o 90o 240o 300o 12 108o O A O B O A A A O 2.4 O 6 12 10√2 B B Fraction of circle: Fraction of circle: Fraction of circle: Fraction of circle: Fraction of circle: ¼ 2/3 5/6 1/3 3/10 Fraction ● circumference Fraction ● circumference Fraction ● circumference 5/6 ● 24π ¼ ● 12π 2/3 ● 24π 1/3 ● 4.8π 3/10 ● 20√2π 20π units 3π units 16π units 1.6π units 6√2π units Fraction ● area Fraction ● area Fraction ● area Fraction ● area Fraction ● area 5/6 ● 144π ¼ ● 36π 2/3 ● 144π 1/3 ● 5.76π 3/10 ● 200π 120π units2 376.8 9π units2 28.26 96π units2 301.44 1.92π units2 6.03 60π units2 188.4

  10. 6. The area of sector AOB is 48π and . Find the radius of ○O. m πr2 Area of a sector = 360 270 48π = πr2 360 4 16 4 3 r2 48 = 3 4 3 r2 64 = r = 8

  11. 7. The area of sector AOB is and . Find the radius of ○O. m πr2 Area of a sector = 360 9 40 π = πr2 4 360 9 9 9 1 = r2 1 1 4 9 81 = r2 4 9 r = 2

  12. Sections Let’s talk pizza

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

  14. 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

  15. 60˚ 8 12 6 30 4 60 8. 9. 10. 11. O O O 160 9π - 18 units2 24π - 36√3 units2 8π - 8√3 units2 π units2 3

  16. Some common fractions and measures! 3/10 1/10 60o 300o 240o 1/3 1/12 330o 45o 225o