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8-8 Arc Length and Circumference

8-8 Arc Length and Circumference. 8-8 Arc Length and Circumference. A circle’s perimeter is called its circumference and is p times the circle’s diameter. 8-8 Arc Length and Circumference. Definition of p p = C /d , where C is the circumference and d the diameter of a circle.

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8-8 Arc Length and Circumference

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  1. 8-8 Arc Length and Circumference

  2. 8-8 Arc Length and Circumference A circle’s perimeter is called its circumference and is p times the circle’s diameter.

  3. 8-8 Arc Length and Circumference Definition of p p= C/d , where C is the circumference and d the diameter of a circle.

  4. 8-8 Arc Length and Circumference Circle Circumference Formula If a circle has circumference C, diameter d, and radius r, then C = pd or C = 2pr.

  5. 8-8 Arc Length and Circumference For a ceiling fan, the tip of a blade travels in a circle with a diameter of 46 inches. For a desk fan, the tip of a blade travels in a circle with a diameter of 6.5 inches. Find the exact circumference of each circle. Find the circumference of each circle to the nearest hundredth of an inch.

  6. 8-8 Arc Length and Circumference For a ceiling fan, the tip of a blade travels in a circle with a diameter of 46 inches. For a desk fan, the tip of a blade travels in a circle with a diameter of 6.5 inches. Find the exact circumference of each circle. C = pdC = pd C = 46p inches C = 6.5p inches

  7. 8-8 Arc Length and Circumference For a ceiling fan, the tip of a blade travels in a circle with a diameter of 46 inches. For a desk fan, the tip of a blade travels in a circle with a diameter of 6.5 inches. Find the circumference of each circle to the nearest hundredth of an inch. C = pdC = pd C = 46p inches C = 6.5p inches C = 144.51 inches C = 20.42inches

  8. 8-8 Arc Length and Circumference Suppose the tip of the ceiling fan blade (d = 46 inches) moves at a rate of 5 revolutions per second and the tip of the desk fan blade (d = 6.5 inches) moves at a rate of 150 revolutions per second. Which travels further, the tip of the ceiling fan blade in 45 seconds or the tip of the desk fan blade in 10 seconds? By how much, rounded to the nearest inch?

  9. 8-8 Arc Length and Circumference Suppose the tip of the ceiling fan blade (d = 46 inches) moves at a rate of 5 revolutions per second and the tip of the desk fan blade (d = 6.5 inches) moves at a rate of 150 revolutions per second. Which travels further, the tip of the ceiling fan blade in 45 seconds or the tip of the desk fan blade in 10 seconds? D = vtcD = vtc D = 5 * 45 * 46pD = 150 * 10 * 6.5p D = 10,350p inches D = 9,750p inches

  10. 8-8 Arc Length and Circumference Suppose the tip of the ceiling fan blade (d = 46 inches) moves at a rate of 5 revolutions per second and the tip of the desk fan blade (d = 6.5 inches) moves at a rate of 150 revolutions per second. By how much, rounded to the nearest inch? D = 10,350p inches D = 9,750p inches Difference = 10,350p – 9,750p Difference = 600p inches» 1,885 inches

  11. 8-8 Arc Length and Circumference Computing Arc Length length of arc = degree measure of arc /360º · C = degree measure of arc /360º · 2πr

  12. 8-8 Arc Length and Circumference In çT, TP = 18 centimeters and mÐPTQ = 50º. Find the exact length of arcPQ. length of arc = degree measure of arc /360º · 2πr =(50/360) * 2p 18 = (50*2*18)/360 * p = (1800/360) p = 5 p centimeters

  13. 8-8 Arc Length and Circumference A circle has a radius of 8 inches. A wedge of the circle has an arc length of 8 inches. What angle, to the nearest tenth of a degree, is formed by the two radii of the wedge? length of arc = degree measure of arc /360º · 2πr 8 =(x/360) * 2p 8 (8 * 360) / 2p 8 = x (2880/16p) = x degree measure of arc » 57.3o

  14. 8-8 Arc Length and Circumference Imagine a rope encompassing Earth’s equator at the surface. Then ask them to imagine lengthening the rope and raising it so every part of the rope is 1 foot above the surface. How much more rope is needed?

  15. 8-8 Arc Length and Circumference A 10º arc of a circle has a length of 6 centimeters. Find the lengths of arcs in that circle if the measure of the arc is 20º, 90º, and 180º. Find the circumference, diameter, and radius of each circle.

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