Sec. 10.6 Circumference and Arc Length p.649 Objectives: Find circumference and arc length. Vocabulary: circumference, arc length, radius, diameter, measure of an arc

Review of Circles Find each measure. RT 54

Review circumference (distance around) of a circle: C = πd or C = 2πr

a. C = 2 πr = 2 π 9 = 18 π 56.55 cm Find the indicated measures. Circumference of a circle with radius 9 centimeters a. C = 2 πr = 2 π 9 = 18 π 56.55 cm

Find the indicated measures. Radius of a circle with circumference 26 meters C = 2 πr = 2 πr 26 = 26 2π r r 4.14

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

The length of an arc is a fraction of the circumference of the circle.

Find the length of each red arc. Arc length = 2πr (m˚/360˚) 60° 360° = a. Arc length of AB 2π(8) ≈ 8.38 centimeters

Find the length of each red arc. b. Arc length = 2πr (m˚/360˚) 60° 360° = b. Arc length of EF 2π(11) ≈ 11.52 centimeters

Find the length of each red arc. Arc length = 2πr (m˚/360˚) 2π(11) 120° 360° = c. Arc length of GH ≈ 23.04 centimeters

Find each arc length. Give answers to the nearest hundredth. FG  18.71 cm Arc length = 2πr (m˚/360˚)

Find each arc length. Give answers to the nearest hundredth. an arc with measure 62 in a circle with radius 2 m Arc length = 2πr (m˚/360˚)  2.16 m

Find each arc length. Give your answer rounded to the nearest hundredth. GH  4.19 m

Find each measure. Give answers to the nearest hundredth. length of NP  7.85 in.

Use arc lengths to find measures 1. Circumference C of Z Arc length = 2πr (m˚/360˚) Arc length = C (m˚/360˚) Arc length of XY 1. 360° m XY = C 4.19 = C(40/360) (360/40) 4.19 = C(40/360)(360/40) 37.71 = C

Arc length = 2πr (m˚/360˚) Find the indicated measure. 2. m RS Arc length of RS (2 r) 360° 2. m RS = 44 (2 (15.28)) m RS 360° = 44 (2 (15.28)) 360° = m RS 15840 (2 15.28) = m RS 165° m RS

Arc length = 2πr (m˚/360˚) Find the indicated measure. 3. Length of PQ Arc length = πd (m˚/360˚) about 5.89 yd

Arc length = C (m˚/360˚) 61.26= (C) 270˚ 360˚ 61.26(360) = C (270˚) 4. Circumference of N N. Arc length = C (m˚/360˚) 61.26= (C) 270˚ 360˚ 81.68 m 61.26(360) = C (270˚)

Arc length = 2πr (m˚/360˚) 10.5= 2πr (150˚/360˚) 5. Radius of G Arc length = 2πr (m˚/360˚) 10.5= 2πr (150˚/360˚) 10.5(360) = 2πr (150˚) about 4.01 ft.