Holt CA Course 1 10-2 Circles and Circumference MG1.1 Understand the concept of a constant such as  ; know the formulas for the circumference and area.

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

Holt CA Course Circles and Circumference Vocabulary *circle center radius (radii) diameter *circumference *pi

Holt CA Course 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

Holt CA Course 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

Holt CA Course Circles and Circumference Diameter A 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. Center Radius Diameter

Holt CA Course Circles and Circumference Circumference The distance around a circle. Center Radius Diameter Circumference

Holt CA Course Circles and Circumference Teacher Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. N The center is point Z, so this is circle Z. LM is a diameter.ZL, ZM, and ZN are radii. M Z L

Holt CA Course Circles and Circumference Student Practice 1: Name the circle, a diameter, and three radii. The center is point D, so this is circle D. IG is a diameter.DI, DG, and DH are radii. G H D I

Holt CA Course 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 The decimal representation of pi starts with and goes on forever without repeating. Most people approximate  using either 3.14 or. 22 7

Holt CA Course Circles and Circumference 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. C d =  C d C d · d =  · d C = dC = (2r) = 2r

Holt CA Course Circles and Circumference Teacher Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by using as an estimate for . C = dC  10.5C  33 ft The circumference of the target is about 33 feet. Use the formula. Replace  with and d with ft 22 7

Holt CA Course Circles and Circumference Student Practice 2: A concrete chalk artist is drawing a circular design. Estimate the circumference of the chalk design by using as an estimate for . C = dC  14 C ≈ 44 in. The circumference of the chalk design is about 44 inches. Use the formula. Replace  with and d with in. 1 2

Holt CA Course Circles and Circumference Use as an estimate for  when the diameter or radius is a multiple of Helpful Hint

Holt CA Course Circles and Circumference Teacher Example 3A: 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 . d = 11 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with ft

Holt CA Course Circles and Circumference Teacher Example 3B: 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 . r = 5 cm; C = ? C = 2rC  C  cm Write the formula. Replace  with 3.14 and r with 5. 5 cm

Holt CA Course Circles and Circumference Student Practice 3A: A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for . d = 9 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with 9. 9 ft

Holt CA Course Circles and Circumference Student Practice 3B: B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for . r = 6 cm; C = ? C = 2rC  C  cm Write the formula. Replace  with 3.14 and r with 6. 6 cm

Holt CA Course Circles and Circumference Lesson Quiz Find the circumference of each circle. Use 3.14 as an estimate for  Find the circumference of a circle with diameter of 20 feet. Use 3.14 as an estimate t for .