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Notes 74: (11.4 ) Circumference and Arc Length

Notes 74: (11.4 ) Circumference and Arc Length. THEOREM 11.8: CIRCUMFERENCE OF A CIRCLE. The circumference C of a circle is C = 2  r or C =  d, where d is the diameter of the circle and r is the radius of the circle . C = 2  r =  d. ARC LENGTH COROLLARY.

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Notes 74: (11.4 ) Circumference and Arc Length

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  1. Notes 74: (11.4) Circumference and Arc Length

  2. THEOREM 11.8: CIRCUMFERENCE OF A CIRCLE • The circumference C of a circle is C = 2r or C = d, where d is the diameter of the circle and r is the radius of the circle. C= 2r = d

  3. 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°.

  4. Example 1 Find the indicated measure. • a. Circumference of a circle with radius 11 meters • b. Radius of a circle with circumference 18 yards

  5. Example 1 Find the indicated measure. • c. The exact radius of a circle with circumference 74 centimeters • d. The exact diameter of a circle with circumference 58 feet

  6. Example 2 • The dimensions of the skateboard wheel shown at the right are in millimeters. To the nearest meter, how far does the wheel travel when it makes 35 revolutions?

  7. Example 3 Find the indicated measure. arc ABRadius of Q

  8. Example 4 A conveyor belt for luggage at an airport is shown at the right. The outer part of the belt forms a 180° arc at each end. For each arc, the radius is 8 feet. Approximate the distance around the belt for a coin on the outer portion. Round to the nearest foot. ABCD ~ WXYZ

  9. Independent Practice 1 of 4 Find the circumference of a circle with diameter 23 inches.

  10. Independent Practice 2 of 4 A skateboard wheel has a diameter of 56 millimeters. How many revolutions does the wheel make when traveling 3 meters?

  11. Independent Practice 3 of 4 Arc length of arc AB Circumference of Z

  12. Independent Practice 4 of 4 The inner portion of the belt also has 180° arcs on each end. The radius of each arc is 4 feet. Find the distance around the belt for a coin on the inner portion. Round to the nearest foot.

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