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Understanding Circles and Circumference: Lessons and Formulas

Learn to identify circle parts, calculate circumference, and solve problems involving radius and diameter changes.

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Understanding Circles and Circumference: Lessons and Formulas

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  1. 9-8 Circles and Circumference Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 9-8 Circles and Circumference Course 1 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. 9-8 Circles and Circumference Course 1 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. 9-8 Circles and Circumference Course 1 Learn to identify the parts of a circle and to find the circumference of a circle.

  5. 9-8 Circles and Circumference Course 1 Insert Lesson Title Here Vocabulary circle center radius (radii) diameter circumference pi

  6. 9-8 Circles and Circumference Center Course 1 A circle is the set of all points in a plane that are the same distance from a given point, called the center.

  7. 9-8 Circles and Circumference Radius Center Course 1 A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii).

  8. 9-8 Circles and Circumference Radius Center Diameter Course 1 A diameteris 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.

  9. 9-8 Circles and Circumference The circle is circle Z. LM is a diameter. ZL, ZM, and ZN are radii. Course 1 Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. L Z M N

  10. 9-8 Circles and Circumference D G I H The circle is circle D. IG is a diameter. DI, DG, and DH are radii. Course 1 Check It Out: Example 1 Name the circle, a diameter, and three radii.

  11. 9-8 Circles and Circumference Circumference Radius Center Diameter Course 1 The distance around a circle is called the circumference.

  12. 9-8 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 C d d Course 1

  13. 9-8 Circles and Circumference Course 1 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 The formula for the circumference of a circle is C = d, or C = 2r.

  14. 9-8 Circles and Circumference 8 ft C = d C 3•8 C 24 ft Course 1 Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding p to 3. Write the formula. Replace  with 3 and d with 8.

  15. 9-8 Circles and Circumference 14 yd C = d C 3•14 C 42 yd Course 1 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.

  16. 9-8 Circles and Circumference C = d C 3.14•11 C 34.54 ft Course 1 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.

  17. 9-8 Circles and Circumference C = 2r C 2 •3.14 •5 C 31.4 cm Course 1 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.

  18. 9-8 Circles and Circumference _______ _______  21.983.14d 7.00 cm d 21.983.14d 3.143.14 Course 1 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.

  19. 9-8 Circles and Circumference C = d C 3.14•9 C 28.26 ft Course 1 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.

  20. 9-8 Circles and Circumference C = 2r C 2 •3.14 •6 C 37.68 cm Course 1 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.

  21. 9-8 Circles and Circumference _______ _______  18.843.14d 6.00cm d 18.843.14d 3.143.14 Course 1 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.

  22. 9-8 Circles and Circumference Course 1 Insert Lesson Title Here 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 . 3 in. 8 in. C = 25.12 in. C = 18.84 in. 62.8 ft

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