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MM2G3c

Standard. MM2G3c Use the properties of circles to solve problems involving the length of an arc and the area of a sector. Circumference of a Circle. The distance around the circle. Theorem 6.19. The circumference C of a circle is: C = d or C = 2 r

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MM2G3c

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  1. Standard MM2G3c Use the properties of circles to solve problems involving the length of an arc and the area of a sector

  2. Circumference of a Circle The distance around the circle

  3. Theorem 6.19 The circumference C of a circle is: C = d or C = 2 r Where d is the diameter of the circle and r is the radius of the circle.

  4. a. C=2 πr =2 π9 56.55 ANSWER The circumference is about 56.55centimeters. EXAMPLE 1 Find the indicated measures. a. Circumference of a circle with radius 9 centimeters SOLUTION Write circumference formula. Substitute 9 forr. =18 π Simplify. Use a calculator.

  5. 26 2 πr = 26 r = 2π 4.14 r ANSWER The radius is about 4.14meters. EXAMPLE 1 Find the indicated measures. b. Radius of a circle with circumference 26 meters C =2 πr Write circumference formula. Substitute 26 for C. Divide each side by 2π. Use a calculator.

  6. The dimensions of a car tire are shown at the right. To the nearest foot, how far does the tire travel when it makes15revolutions? = 15 + 2 (5.5) d C = πd EXAMPLE 2 Tire Revolutions SOLUTION Find the diameter of the tire STEP 1 = 26 in. Find the circumference of the tire STEP 2 =π(26) ≈81.68in.

  7. 15 81.68 in. 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. = 1225.2 in.

  8. 1 ft 1225.2 in. = 102.1 ft 12 in. ANSWER The tire travels approximately 102 feet. EXAMPLE 2 STEP 4 Use unit analysis. Change 1225.2 inches tofeet.

  9. ANSWER about 15.71in.; about5.41 feet GUIDED PRACTICE • Find the circumference of a circle with diameter 5 inches. • Find the diameter of a circle with circumference 17 feet.

  10. ANSWER about 69.1feet; about23.9 meters GUIDED PRACTICE • Find the circumference of a circle with a radius of 11 feet. • Find the diameter of a circle with circumference 75 meters.

  11. ANSWER about 15.71in.; about5.41 feet GUIDED PRACTICE • Find the circumference of a circle with diameter 5 inches.

  12. ANSWER about GUIDED PRACTICE • What is the measure of the radius in the circle below?

  13. Arc Length A portion of the circumference of a circle

  14. Arc Length Corollary In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°

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

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

  17. 120° c. 2π(1) Arc length of GH = 360° c. EXAMPLE 3 Find the length of each red arc. SOLUTION ≈ 23.04 centimeters

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

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

  20. You Try! Find the indicated measure. 1. arc AB

  21. You Try! Find the indicated measure. 2. circumference of circle Q

  22. You Try! Find the indicated measure. 1. radius of circle N

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