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Circles and Circumference - Understanding the Parts and Formula

Learn about circles, their components like radius and diameter, and the formula to calculate the circumference. Practice finding the circumference using real-life examples in this introductory course.

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Circles and Circumference - Understanding the Parts and Formula

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  1. 10-1 Circles and Circumference

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

  3. 10-1 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).

  4. 10-1 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.

  5. 10-1 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

  6. 10-1 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.

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

  8. 10-1 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

  9. 10-1 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.

  10. 10-1 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.

  11. 10-1 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.

  12. 10-1 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.

  13. 10-1 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.

  14. 10-1 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.

  15. 10-1 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.

  16. 10-1 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.

  17. 10-1 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.

  18. 10-1 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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