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

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Presentation on theme: "Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π 2. 120 360 (9π) 1. 45 360."— Presentation transcript:

1 Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π (9π)

2 Warm-Up Exercises Simplify the expression. ANSWER 5π5π 5π5π 3 3. π (15π)

3 Warm-Up Exercises Simplify the expression. 5. A central angle of a circle measures 82º. Find the measure of the intercepted arc. 6. Solve 3.8 x = ANSWER 82º ANSWER 11.4

4 Warm-Up Exercises EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. = 2 π 9 = 18 π a. Circumference of a circle with radius 9 centimeters SOLUTION The circumference is about centimeters. ANSWER a.a. C = 2 πr

5 Warm-Up Exercises EXAMPLE 1 Use the formula for circumference 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. ANSWER Find the indicated measures. b. Radius of a circle with circumference 26 meters

6 Warm-Up Exercises EXAMPLE 2 Use circumference to find distance traveled 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 = (5.5) = 26 in. C= πd = π(26)≈ in.

7 Warm-Up Exercises EXAMPLE 2 Use circumference to find distance traveled 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 in. = in.

8 Warm-Up Exercises EXAMPLE 2 Use circumference to find distance traveled STEP 4 Use unit analysis. Change inches to feet. The tire travels approximately 102 feet. ANSWER in. 1 ft 12 in. = ft

9 Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 1. Find the circumference of a circle with diameter 5 inches. Find the diameter of a circle with circumference 17 feet. about in.; about 5.41 feet ANSWER

10 Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 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 Warm-Up Exercises EXAMPLE 3 Find arc lengths Find the length of each red arc. a. SOLUTION a. Arc length of AB 2π(8) 60 ° 360 ° = ≈ 8.38 centimeters

12 Warm-Up Exercises EXAMPLE 3 Find arc lengths Find the length of each red arc. b. SOLUTION b. Arc length of EF 2π(11) 60 ° 360 ° = ≈ centimeters

13 Warm-Up Exercises EXAMPLE 3 Find arc lengths Find the length of each red arc. c. SOLUTION c. Arc length of GH 2π(1) 120 ° 360 ° = ≈ centimeters

14 Warm-Up Exercises EXAMPLE 4 Find arc lengths to find measures Find the indicated measure. a. Circumference C of Z SOLUTION = C 4.19 C 9 1 = Arc length of XY C a. 360 ° m XY = 4.19 C 360 ° 40 ° =

15 Warm-Up Exercises EXAMPLE 4 Find arc lengths to find measures Find the indicated measure. b. m RS Arc length of RS 2 r 360 ° b. m RS = SOLUTION 44 2 (15.28) m RS 360 ° = 44 2 (15.28) 360 ° = m RS 165 ° m RS

16 Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 Find the indicated measure. 3. Length of PQ about 5.89 yd ANSWER

17 Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 4. Circumference of N m ANSWER Find the indicated measure.

18 Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 5. Radius of G Find the indicated measure. about 4.01 ft.ANSWER

19 Warm-Up Exercises EXAMPLE 5 Find arc lengths to find distance 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 Warm-Up Exercises EXAMPLE 5 Find arc lengths to find distance = 2(84.39) + 2 2π ≈ meters The runner on the red path travels about 400 meters. ANSWER

21 Warm-Up Exercises GUIDED PRACTICE for Example 5 6. In Example 5, the radius of the arc for a runner on the blue path is 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 meters ANSWER

22 Warm-Up Exercises Daily Homework Quiz Find the indicated measure. 1. Circumference ANSWER about in.

23 Warm-Up Exercises Daily Homework Quiz ANSWER about 7.64 ft 2. Radius C = 48 ft

24 Warm-Up Exercises Daily Homework Quiz 3. Length of AB ANSWER 8.64 cm

25 Warm-Up Exercises Daily Homework Quiz 4. Find the total circumference of the circles. ANSWER cm

26 Warm-Up Exercises Daily Homework Quiz Find the indicated measure. 5. Radius ANSWER about cm

27 Warm-Up Exercises Daily Homework Quiz 6. Circumference ANSWER about in.


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