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

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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 = 120 360. ANSWER 82º ANSWER 11.4

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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 56.55 a. Circumference of a circle with radius 9 centimeters SOLUTION The circumference is about 56.55 centimeters. ANSWER a.a. C = 2 πr

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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

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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 = 15 + 2 (5.5) = 26 in. C= πd = π(26)≈ 81.68 in.

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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. 15 81.68 in. = 1225.2 in.

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Warm-Up Exercises EXAMPLE 2 Use circumference to find distance traveled STEP 4 Use unit analysis. Change 1225.2 inches to feet. The tire travels approximately 102 feet. ANSWER 1225.2 in. 1 ft 12 in. = 102.1 ft

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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 15.71 in.; about 5.41 feet ANSWER

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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

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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

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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 ° = ≈ 11.52 centimeters

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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 ° = ≈ 23.04 centimeters

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Warm-Up Exercises EXAMPLE 4 Find arc lengths to find measures 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 ° =

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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

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

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Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 4. Circumference of N 81.68 m ANSWER Find the indicated measure.

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

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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.

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Warm-Up Exercises EXAMPLE 5 Find arc lengths to find distance = 2(84.39) + 2 2π 36.8 1 2 ≈ 400.0 meters The runner on the red path travels about 400 meters. ANSWER

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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 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

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Warm-Up Exercises Daily Homework Quiz Find the indicated measure. 1. Circumference ANSWER about 81.68 in.

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

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

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Warm-Up Exercises Daily Homework Quiz 4. Find the total circumference of the circles. ANSWER 100.53 cm

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Warm-Up Exercises Daily Homework Quiz Find the indicated measure. 5. Radius ANSWER about 21.88 cm

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Warm-Up Exercises Daily Homework Quiz 6. Circumference ANSWER about 222.72 in.

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11.4 Circumference and Arc Length

11.4 Circumference and Arc Length

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