1. 10-1 Circles and Circumference

2. A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center 10-1 Circles and Circumference

3. A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Center Radius Course 1 10-1 Circles and Circumference

4. A diameter is a line segment that passes through the center of the circle and has both endpoints on the circle. The length of the diameter is twice the length of the radius. Center Radius Diameter Course 1 10-1 Circles and Circumference

5. Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. N The circle is circle Z.LM is a diameter.ZL, ZM, and ZN are radii. M Z L Course 1 10-1 Circles and Circumference

6. Check It Out: Example 1 Name the circle, a diameter, and three radii. The circle is circle D. IG is a diameter.DI, DG, and DH are radii. G H D I Course 1 10-1 Circles and Circumference

7. The distance around a circle is called the circumference. Center Radius Diameter Circumference Course 1 10-1 Circles and Circumference

8. The ratio of the circumference to the diameter,, is the same for any circle. This ratio is represented by the Greek letter , which is read “pi.” C d C d =  Course 1 10-1 Circles and Circumference

9. The formula for the circumference of a circle is C = d, or C = 2r. The decimal representation of pi starts with 3.14159265... and goes on forever without repeating. We estimate pi using either 3.14 or. 22 7 Course 1 10-1 Circles and Circumference

10. Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding  to 3. C = dC  3 8C  24 ft Write the formula. Replace  with 3 and d with 8. 8 ft Course 1 10-1 Circles and Circumference

11. Check It Out: Example 2 A second skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding  to 3. C = dC  3 14C  42 yd Write the formula. Replace  with 3 and d with 14. 14 yd Course 1 10-1 Circles and Circumference

12. Additional Example 3A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 11 ft; C = ? C = dC  3.14 11C  34.54 ft Write the formula. Replace  with 3.14 and d with 11. 11 ft Course 1 10-1 Circles and Circumference

13. Additional Example 3B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 5 cm; C = ? C = 2rC  2 3.14 5C  31.4 cm Write the formula. Replace  with 3.14 and r with 5. 5 cm Course 1 10-1 Circles and Circumference

14. Additional Example 3C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C = 21.98 cm; d = ? C = d 21.98  3.14d7.00 cm  d Write the formula. Replace C with 21.98 and  with 3.14. 21.98 3.14d _______ 3.14 3.14  Divide both sides by 3.14. Course 1 10-1 Circles and Circumference

15. Check It Out: Example 3A Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 9 ft; C = ? C = dC  3.14 9C  28.26 ft Write the formula. Replace  with 3.14 and d with 9. 9 ft Course 1 10-1 Circles and Circumference

16. Check It Out: Example 3B Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 6 cm; C = ? C = 2rC  2 3.14 6C  37.68 cm Write the formula. Replace  with 3.14 and r with 6. 6 cm Course 1 10-1 Circles and Circumference

17. Check It Out: Example 3C Find each missing value to the nearest hundredth. Use 3.14 for pi. C = 18.84 cm; d = ? C = d 18.84  3.14d6.00 cm  d Write the formula. Replace C with 18.84 and  with 3.14. 18.84 3.14d _______ 3.14 3.14  Divide both sides by 3.14. Course 1 10-1 Circles and Circumference

18. Lesson Quiz Find the circumference of each circle. Use 3.14 for . 1. 2. 3. Find the circumference of a circle with diameter of 20 feet. Use 3.14 for . C = 25.12 in. Insert Lesson Title Here C = 18.84 in. 8 in. 62.8 ft 3 in. Course 1 10-1 Circles and Circumference