1. 8-7 Circles and Circumference Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 8-7 Circles and Circumference Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change. The perimeter is multiplied by 5, and the area is multiplied by 25.

3. 8-7 Circles and Circumference Problem of the Day When using a calculator to find the width of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct width? 1.3

4. 8-7 Circles and Circumference Vocabulary circle center chord diameter radius (radii) ‏ circumference pi

5. 8-7 Circles and Circumference A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center

6. 8-7 Circles and Circumference Radius (plural: radii). A line segment with one endpoint at the center of the circle and the other endpoint on the circle. Center Radius

7. 8-7 Circles and Circumference A diameter is a chord that passes through the center of the circle. Diameters are the longest chords in a circle. Center Radius Diameter

8. 8-7 Circles and Circumference A chord is a line segment that has both endpoints on the circle. Center Radius Diameter Chord

9. 8-7 Circles and Circumference 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.LN and LM are chords. M Z L ZL, ZM, and ZN are radii.

10. 8-7 Circles and Circumference Check It Out: Example 1 Point D is the center of the circle. Name the circle, two chords, a diameter, and three radii. The circle is circle D.Radii = DI, DG, and DH are diameter = GI chords = GI and GH G D H I

11. 8-7 Circles and Circumference The distance around a circle is called the circumference. Center Radius Diameter Circumference

12. 8-7 Circles and Circumference 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 = 

13. 8-7 Circles and Circumference 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. Most people estimate  using either 3.14 or. 22 7

14. 8-7 Circles and Circumference 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 The circumference of the target is about 24 feet.

15. 8-7 Circles and Circumference C = dC  3 4C  12 ft A carpenter is building a circular tabletop. Estimate the circumference of the tabletop by rounding to 3.  Check It Out: 2A What is the circumference of the tabletop if the diameter is 4 feet? 

16. 8-7 Circles and Circumference C = 2rC  2 3 3C  18 ft carpenter is building a circular tabletop. Estimate the circumference of the tabletop by rounding to 3.  What is the circumference of the tabletop if the radius is 3 feet? Check It Out: 2B

17. 8-7 Circles and Circumference 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 11 C  34.54 ft Write the formula. Replace  with 3.14 and d with 11. 11 ft

18. 8-7 Circles and Circumference Additional Example 3B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 22/7 for pi. r = 7 cm; C = ? C = 2rC  2 22/7 7 C  44 cm Write the formula. Replace  with 22/7 and r with 7. 7 cm

19. 8-7 Circles and Circumference Check It Out: Example 3A Find the missing value to the nearest hundredth. Use 3.14 or 22for pi. C = ? 7 D = 2.8 C = πd C ≈ 3.14 2.8 C ≈ 8.79 m

20. 8-7 Circles and Circumference Check It Out: Example 3B Find the missing value to the nearest hundredth. Use 3.14 or 22for pi. r = ? 7 C = 88 cm C = 2πr 88 ≈ 2 r 88 ≈ 44 r r ≈ 14 cm 22 7 __ 7

21. 8-7 Circles and Circumference Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

22. 8-7 Circles and Circumference Lesson Quiz Find the circumference of each circle. Use 3.14 for . 1. 2. 3. Find the circumference of a circle with a diameter of 20 feet. Use 3.14 for . C  25.12 in.C  18.84 in. 8 in. 62.8 ft 3 in.

23. 8-7 Circles and Circumference 1. Identify the circumference of the given circle. Use 3.14 for . A. 31.14 in. B. 31.21 in. C. 31.33 in. D. 31.4 in. Lesson Quiz for Student Response Systems 10 in.

24. 8-7 Circles and Circumference 2. Identify the circumference of the given circle. Use 3.14 for . A. 37.54 in. B. 37.68 in. C. 37.81 in. D. 37.93 in. Lesson Quiz for Student Response Systems 6 in.

25. 8-7 Circles and Circumference 3. Identify the circumference of a circle with a diameter of 26 feet. Use 3.14 for . A. 81.64 ft B. 81.73 ft C. 81.86 ft D. 81.92 ft Lesson Quiz for Student Response Systems