Exit Ticket Sample Solutions 1. Find the arc length of. ( )= ()() ( )=. ( ) = The arc length of is (. ) or.. Homework Problem Set Sample Solutions S.79 1. and are points on the circle of radius, and the measure of is. Find, to one decimal place, each of the following. a. The length of ( )= ( ) ( )= The arc length of is or approximately.. b. The ratio of the arc length to the radius of the circle = : Arc Length Unit 11: Circles and Chords 125 This file derived from GEO--TE-1.3.0-10.2015
c. The length of chord The length of is twice the value of in. = = = Chord has a length of or approximately.. d. The distance of the chord from the center of the circle The distance of chord from the center of the circle is labeled as in. = The distance of chord from the center of the circle is, or approximately. e. The perimeter of sector ( ) = + + ( ) = + The perimeter of sector is ( + ), or approximately.. 2. What is the radius of a circle if the length of a arc is? = () = The radius of the circle is. : Arc Length Unit 11: Circles and Chords 126 This file derived from GEO--TE-1.3.0-10.2015
S.80 3. In the circles shown, find the value of. Figures are not drawn to scale. A. B. C. = 6 = 18 5 = 2 45 4. The concentric circles all have center. The measure of the central angle is. The arc lengths are given. a. Find the radius of each circle. Radius of inner circle: =, = Radius of middle circle: =, = Radius of outer circle: =, = b. Determine the ratio of the arc length to the radius of each circle. is the ratio of the arc length to the radius of each circle. Teacher note: It is the measure of the central angle in radians. : Arc Length Unit 11: Circles and Chords 127 This file derived from GEO--TE-1.3.0-10.2015
5. In the figure, if the length of is, find the length of. Since is. of, then the arc length of is of ; the arc length of is S.81 6. Given circle with, find the following (round to the nearest hundredth, if necessary). a. b. c.. d. Arc length.. e. Arc length.. f. Arc length.. 7. Given circle, find the following (round to the nearest hundredth, if necessary). a. Circumference of circle. b. Radius of circle.. : Arc Length Unit 11: Circles and Chords 128 This file derived from GEO--TE-1.3.0-10.2015
S.82 8. Many large cities are building or have built mega Ferris wheels. One is feet in diameter and has cars each seating up to people. Each time the Ferris wheel turns degrees, a car is in a position to load. a. What is the value of in degrees? =. b. How far does a car move with each rotation of degrees (round to the nearest whole number)? = ().. 9. Find the radius of the circle A, as well as,, and (leave arc length in terms of pi). Note that and do not lie on a diameter. Let r be defined as the radius. 360 30 2r 4 r = cm y y x 360 x 24 2 10 x = 75 360 y 24 2 18 y = 135 CAE = 360-75 - 135-30 = 120 360 120 24 2 z =16 cm : Arc Length Unit 11: Circles and Chords 129 This file derived from GEO--TE-1.3.0-10.2015
: Arc Length Unit 11: Circles and Chords 130 This file derived from GEO--TE-1.3.0-10.2015