1. 11.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Circumference and Arc Length

2. 11.4 Warm-Up Simplify the expression. ANSWER 1 8 3π3π 2. 120 360 (9π) 1. 45 360

3. 11.4 Warm-Up Simplify the expression. ANSWER 5π5π 5π5π 3 3. π 15 3 4. 60 360 (15π)

4. 11.4 Warm-Up 5. A central angle of a circle measures 82º. Find the measure of the intercepted arc. 6. Solve 3.8 x = 120 360. ANSWER 82º ANSWER 11.4

5. Example 1 Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. = 2 π 9 = 18 π 56.55 a. Circumference of a circle with radius 9 centimeters SOLUTION The circumference is about 56.55 centimeters. a.a. C = 2 πr

6. 11.4 Example 1 Find the indicated measures. Write circumference formula. Substitute 26 for C. Divide each side by 2π. Use a calculator. r 4.14 = 2 πr26 = 2π2π r C = 2 πr The radius is about 4.14 meters. b. Radius of a circle with circumference 26 meters SOLUTION

7. 11.4 Example 2 The dimensions of a car tire are shown at the right. To the nearest foot, how far does the tire travel when it makes 15 revolutions? STEP 1 Find the diameter of the tire STEP 2 Find the circumference of the tire Tire Revolutions SOLUTION d = 15 + 2 (5.5) = 26 in. C= πd = π(26)≈ 81.68 in.

8. 11.4 Example 2 STEP 3 Find the distance the tire travels in 15 revolutions. In one revolution, the tire travels a distance equal to its circumference. In 15 revolutions, the tire travels a distance equal to 15 times its circumference. 15 81.68 in. = 1225.2 in.

9. 11.4 Example 2 STEP 4 Use unit analysis. Change 1225.2 inches to feet. The tire travels approximately 102 feet. 1225.2 in. 1 ft 12 in. = 102.1 ft

10. 11.4 Guided Practice 1. Find the circumference of a circle with diameter 5 inches. Find the diameter of a circle with circumference 17 feet. about 15.71 in.; about 5.41 feet ANSWER 2. A car tire has a diameter of 28 inches. How many revolutions does the tire make while traveling 500 feet? about 68 revolutionsANSWER

11. 11.4 Example 3 Find the length of each red arc. a. SOLUTION a. Arc length of AB 2π(8) 60 ° 360 ° = ≈ 8.38 centimeters

12. 11.4 Example 3 Find the length of each red arc. b. Arc length of EF 2π(11) 60 ° 360 ° = ≈ 11.52 centimeters SOLUTION

13. 11.4 Example 3 Find the length of each red arc. SOLUTION c. Arc length of GH 2π(1) 120 ° 360 ° = ≈ 23.04 centimeters

14. 11.4 Example 4 Find the indicated measure. a. Circumference C of Z SOLUTION 37.71 = C 4.19 C 9 1 = Arc length of XY C a. 360 ° m XY = 4.19 C 360 ° 40 ° =

15. 11.4 Example 4 Find the indicated measure. SOLUTION b. m RS Arc length of RS 2 r 360 ° b. m RS = 44 2 (15.28) m RS 360 ° = 44 2 (15.28) 360 ° = m RS 165 ° m RS

16. 11.4 Guided Practice Find the indicated measure. 3. Length of PQ about 5.89 yd ANSWER

17. 11.4 Guided Practice Find the indicated measure. 4. Circumference of N 81.68 m ANSWER

18. 11.4 Guided Practice Find the indicated measure. about 4.01 ft.ANSWER 5. Radius of G

19. 11.4 Example 5 TRACK The curves at the ends of the track shown are 180° arcs of circles. The radius of the arc for a runner on the red path shown is 36.8 meters. About how far does this runner travel to go once around the track? Round to the nearest tenth of a meter. SOLUTION The path of a runner is made of two straight sections and two semicircles. To find the total distance, find the sum of the lengths of each part.

20. 11.4 Example 5 = 2(84.39) + 2 2π 36.8 1 2 ≈ 400.0 meters The runner on the red path travels about 400 meters.

21. 11.4 Guided Practice 6. In Example 5, the radius of the arc for a runner on the blue path is 44.02 meters, as shown in the diagram. About how far does this runner travel to go once around the track? Round to the nearest tenth of a meter. about 445.4 meters ANSWER

22. 11.4 Lesson Quiz Find the indicated measure. 1. Circumference ANSWER about 81.68 in.

23. 11.4 Lesson Quiz Find the indicated measure. ANSWER about 7.64 ft 2. Radius C = 48 ft

24. 11.4 Lesson Quiz Find the indicated measure. 3. Length of AB ANSWER 8.64 cm

25. 11.4 Lesson Quiz 4. Find the total circumference of the circles. ANSWER 100.53 cm

26. 11.4 Lesson Quiz 5. Radius ANSWER about 21.88 cm Find the indicated measure.

27. 11.4 Lesson Quiz Find the indicated measure. 6. Circumference ANSWER about 222.72 in.