11.4 circumference and arc length

11.4 Circumference and Arc Length

Objectives/Assignment ,[object Object],[object Object]

Finding circumference and arc length ,[object Object]

Theorem 11.6: Circumference of a Circle ,[object Object]

Ex. 1: Using circumference ,[object Object],[object Object]

Solution: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2  a. b.

Arc Length Corollary ,[object Object],Arc length of 2  r = 360 ° or Arc length of = 360 ° • 2  r m m

More . . . ,[object Object],½ • 2  r ¼ • 2  r r r

Ex. 2: Finding Arc Lengths ,[object Object],50 ° a. 50 ° b. 100 ° c.

Ex. 2: Finding Arc Lengths ,[object Object],50 ° a. a. Arc length of = # of ° 360 ° • 2  r  4.36 centimeters a. Arc length of = 50 ° 360 ° • 2  (5)

Ex. 2: Finding Arc Lengths ,[object Object],50 ° b. b. Arc length of = # of ° 360 ° • 2  r b. Arc length of = 50 ° 360 ° • 2  (7)  6.11 centimeters

Ex. 2: Finding Arc Lengths ,[object Object],100 ° c. c. Arc length of = # of ° 360 ° • 2  r c. Arc length of = 100 ° 360 ° • 2  (7)  12.22 centimeters In parts (a) and (b) in Example 2, note that the arcs have the same measure but different lengths because the circumferences of the circles are not equal.

Ex. 3: Using Arc Lengths ,[object Object],60 ° a. circumference Arc length of 2  r = 360 ° 3.82 2  r 6 1 = 3.82 2  r 360° 60° = 3.82(6) = 2  r 22.92 = 2  r C = 2  r; so using substitution, C = 22.92 meters. m

Ex. 3: Using Arc Lengths ,[object Object],b. m Arc length of 2  r = 360 ° 18 2  (7.64) 360° = 135 °  m m m • 360 ° 360 ° •  So the m  135 °

Ex. 4: Comparing Circumferences ,[object Object]

[object Object],[object Object],[object Object],Ex. 4: Comparing Circumferences

[object Object],Ex. 4: Comparing Circumferences TIRE A: 100 ft. 76.03 in. 1200 in. 76.03 in. = 100 ft. 80.11 in. 1200 in. 80.11 in. =  15.8 revolutions TIRE B:  15.0 revolutions

Ex. 5: Finding Arc Length ,[object Object],[object Object],[object Object]

Ex. 5: Finding Arc Length ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Ex. 5: Lane 1 Ex. 5: Lane 2

11.4 circumference and arc length

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