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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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. 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. Learn to identify the parts of a circle and to find the circumference of a circle.

  5. Vocabulary circle center chord diameter radius (radii)‏ circumference pi

  6. Center A circle is the set of all points in a plane that are the same distance from a given point, called the center.

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

  8. Radius Center Diameter A diameteris a chord that passes through the center of the circle. Diameters are the longest chords in a circle.

  9. Radius Center Chord Diameter A chord is a line segment that has both endpoints on the circle.

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

  11. D G I H The circle is circle D. IG is a diameter. IG and IH are chords. DI, DG, and DH are radii. Check It Out: Example 1 Name the circle, a diameter, and three radii.

  12. Circumference Radius Center Diameter The distance around a circle is called the circumference.

  13. 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

  14. 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 The formula for the circumference of a circle is C = d, or C = 2r.

  15. 8 ft C = d C 3•8 C 24 ft 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. Write the formula. Replace  with 3 and d with 8.

  16. 14 yd C = d C 3•14 C 42 yd 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. Write the formula. Replace  with 3 and d with 14.

  17. C = d C 3.14•11 C 34.54 ft 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 = ? 11 ft Write the formula. Replace  with 3.14 and d with 11.

  18. C = 2r C 2 •3.14 •5 C 31.4 cm 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 = ? 5 cm Write the formula. Replace  with 3.14 and r with 5.

  19. 21.983.14d 21.983.14d _______ _______  3.143.14 7.00 cm d 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 Write the formula. Replace C with 21.98 and with 3.14. Divide both sides by 3.14.

  20. C = d C 3.14•9 C 28.26 ft Check It Out: Example 3A Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 9 ft; C = ? 9 ft Write the formula. Replace  with 3.14 and d with 9.

  21. C = 2r C 2 •3.14 •6 C 37.68 cm Check It Out: Example 3B Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 6 cm; C = ? 6 cm Write the formula. Replace  with 3.14 and r with 6.

  22. 18.843.14d 18.843.14d _______ _______  3.143.14 6.00cm d 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 Write the formula. Replace C with 18.84 and with 3.14. Divide both sides by 3.14.

  23. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  24. Lesson Quiz Find the circumference of each circle. Use 3.14 for . 1.2. 3. Find the circumference of a circle with adiameter of 20 feet. Use 3.14 for . 3 in. 8 in. C = 25.12 in. C = 18.84 in. 62.8 ft

  25. Lesson Quiz for Student Response Systems 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. 10 in.

  26. Lesson Quiz for Student Response Systems 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. 6 in.

  27. Lesson Quiz for Student Response Systems 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 ftD. 81.92 ft

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