1. Geometry 11.4 Circumference and Arc Length

2. July 2, 2015Geometry 11.4 Circumference and Arc Length2 Goals  Find the circumference of a circle.  Find the length of an arc.  Solve problems using circumference and arc length.  Conversions involving radians

3. July 2, 2015Geometry 11.4 Circumference and Arc Length3 Circumference The circumference is the distance around a circle.

4. July 2, 2015Geometry 11.4 Circumference and Arc Length4 Circumference You can find the circumference if you know the diameter (d) or the radius (r) of the circle.

5. July 2, 2015Geometry 11.4 Circumference and Arc Length5 Example Find the circumference of a circle with a radius of 8. This is the circumference “in terms of pi”. When computing C in decimal, use 3.14 or the pi button.

6. July 2, 2015Geometry 11.4 Circumference and Arc Length6 Semicircle  Half of a circle.  Its measure is 180.  Its length is one-half the circumference.

7. Converting Degrees to Radians July 2, 2015Geometry 11.4 Circumference and Arc Length7

8. Practice A circle is 360 degrees. How many radians does that equal? July 2, 2015Geometry 11.4 Circumference and Arc Length8

9. Practice A circle is 360 degrees. How many radians does that equal? Think about when we inscribed a hexagon in a circle. July 2, 2015Geometry 11.4 Circumference and Arc Length9

10.  How many radians are in a semicircle? July 2, 2015Geometry 11.4 Circumference and Arc Length10

11. Radians to Degrees July 2, 2015Geometry 11.4 Circumference and Arc Length11

12. Practice July 2, 2015Geometry 11.4 Circumference and Arc Length12

13. Practice July 2, 2015Geometry 11.4 Circumference and Arc Length13

14. July 2, 2015Geometry 11.4 Circumference and Arc Length14 Arc Length The ratio of the length of an arc to the circumference of a circle is equal to the ratio of the measure of the arc to 360. A B Recall: the measure of the arc is equal to the central angle that intercepts it.

15. July 2, 2015Geometry 11.4 Circumference and Arc Length15 ExampleFind the length of AB. A B 5 80 L Write the proportion: Length of Arc Circumference of circle Central Angle

16. July 2, 2015Geometry 11.4 Circumference and Arc Length16 Solve the proportion A B 5 80 L 6.98

17. July 2, 2015Geometry 11.4 Circumference and Arc Length17 Your TurnFind the length of AB A B 8 25 x

18. July 2, 2015Geometry 11.4 Circumference and Arc Length18 Example The length of AB is 25 and the radius is 10. Find the mAB. A B 10 xx 25

19. July 2, 2015Geometry 11.4 Circumference and Arc Length19 Problem 1 An indoor track at a gym has the design below. What is the length of the entire track? 100 ft 40 ft

20. July 2, 2015Geometry 11.4 Circumference and Arc Length20 Problem 1 Solution The ends make one circle. 100 ft 40 ft The diameter is 40 ft. C = (40)

21. July 2, 2015Geometry 11.4 Circumference and Arc Length21 Problem 1 Solution 100 ft 40 ft Add 200 for the straight segments. Perimeter = 40 + 200 ft Or, 325.66 ft.

22. July 2, 2015Geometry 11.4 Circumference and Arc Length22 Summary  The length of an arc on a circle is proportional to the measure of the arc and to the central angle.  A semicircle has 180 and it’s length is half the circumference.