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California Standards

California Standards. MG1.1 Understand the concept of a constant such as p ; know the formulas for the circumference and area of a circle. Also covered: AF1.1, AF3.1, AF3.2, MG1.2. Vocabulary. circle center radius (radii) diameter circumference pi. Center.

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California Standards

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  1. California Standards MG1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle. Also covered:AF1.1, AF3.1, AF3.2, MG1.2

  2. Vocabulary circle center radius (radii) diameter circumference pi

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

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

  5. Radius Center Diameter DiameterA line segment that passes through the center of the circle and has both endpoints on the circle. Notice that the length of the diameter is twice the length of the radius, d = 2r.

  6. Circumference Radius Center Diameter Circumference The distance around a circle.

  7. LM is a diameter. 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 The center is point Z, so this is circle Z.

  8. D G I H IG is a diameter. DI, DG, and DH are radii. Check It Out! Example 1 Name the circle, a diameter, and three radii. The center is point D, so this is circle D.

  9. 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 The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. Most people approximate p using either 3.14 or . 22 7

  10. Because , you can multiply both sides of the equation by d to get a formula for circumference. You can also substitute 2r for d because d = 2r. =  =  · d =  · d C C C d d d C = d C = (2r) = 2pr

  11. C = d C 3.14•11 C 34.54 ft Additional Example 3: Using the Formula for the Circumference of a Circle A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for p. d = 11 ft; C = ? 11 ft Write the formula. Replace  with 3.14 and d with 11.

  12. C = 2r C 2 •3.14 •5 C 31.40 cm Additional Example 3: Using the Formula for the Circumference of a Circle B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. r = 5 cm; C = ? 5 cm Write the formula. Replace  with 3.14 and r with 5.

  13. C = d C 3.14•9 C 28.26 ft Check It Out! Example 3 A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for p. d = 9 ft; C = ? 9 ft Write the formula. Replace  with 3.14 and d with 9.

  14. C = 2r C 2 •3.14 •6 C 37.68 cm Check It Out! Example 3 B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. r = 6 cm; C = ? 6 cm Write the formula. Replace  with 3.14 and r with 6.

  15. _______ _______  18.843.14d 6.00cm d 18.843.14d 3.143.14 Check It Out! Example 3 C. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. 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.

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