CLOCKS Big Ben is a famous clock tower in London, England. The diameter of the clock face is 23 feet. center


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1 3 Circles and Circumference MAIN IDEA Find the circumference of circles. New Vocabulary circle center diameter circumference radius π (pi) CLOCKS Big Ben is a famous clock tower in London, England. The diameter of the clock face is 3 feet. B. Which point appears at the middle of Big Ben? D A. How does the distance from C D A to C compare to the distance from B to D? 3. Find the distance from D to C..5 feet Math Online glencoe.com Extra Examples Personal Tutor SelfCheck Quiz A circle is the set of all points in a plane that are the same distance from a given point, called the center. center The circumference C is the distance around a circle. The diameter d is the distance across a circle through its center. The radius r is the distance from the center to any point on a circle. The diameter of a circle is times the radius, or d = r. Another C relationship that is true of all circles is _ = This d nonterminating and nonrepeating number is represented by the Greek letter π (pi). An approximation often used for π is 3.4. Circumference of a Circle. The distance from B to D is half the distance from A to C. 584 Key Concept Words The circumference C of a circle is equal to its diameter d times π, or times its radius r times π. Symbols C = πd or C = πr When finding the circumference of a circle, it is necessary to use an approximation of π since its exact value cannot be determined. Chapter Measurement: Two and ThreeDimensional Figures 584_0584_0588_CH_L3_ /6/0 :33:40 PM
2 Find Circumference Estimation To estimate the circumference of a circle, you can use 3 for π since π 3. CLOCKS Refer to the lesson opener. Find the circumference of Big Ben s clock face. Estimate C = 3 3 or 69 ft C = πd Circumference of a circle C 3.4 (3) Replace π with 3.4 and d with 3. C. Multiply. So, the distance around the clock is about. feet. Check for Reasonableness. 69 Find the circumference of each circle. Use 3.4 for π. Round to the a. 5. ft b. 9.8 in. 4 ft 63 in. Another approximation for π is _. Use this value when the radius or diameter is a multiple of or has a multiple of in its numerator if the radius is a fraction. Find Circumference Technology You can use a calculator to find the circumference. To find π (), press [π]. The circumference is about Find the circumference of a circle with a radius of inches. Since is a multiple of, use _ for π. C = πr _ Circumference of a circle in. C _ Replace π with and r with. C _ 3 _ Divide by the GCF,. C 3 Simplify. The circumference of the circle is about 3 inches. Find the circumference of each circle. Use for π. c. 0 in. d. _ 5 ft 0 in. 8 ft Lesson 3 Circles and Circumference 585
3 indicates multistep problem Examples, (p. 585) _ Find the circumference of each circle. Use 3.4 or for π. Round to the. 3.4 ft. 36. m 5 ft. m m in. 4 m 4 in. 5. CLOCKS To the nearest tenth, how many centimeters does the tip of the minute hand of the clock shown travel each hour? 6. cm.4 cm HOMEWORK HELP For Exercises 6 9, , 6 9 See Examples Exercise Levels A: 6 B: 35 C: HELP _ Find the circumference of each circle. Use 3.4 or for π. Round to the m. cm ft yd km 50. m 50. ft 36.4 km. radius = _ 3 4 in. in. 3. diameter = 0 _ in. 4. diameter = 5. m 33 in. 5. diameter = 0.8 km 6. radius = _ 5 8 in. _ 6. diameter = _ 4 mi 33.9 km in. 4.4 m 38 _ 8. SPORTS A flying disc has a diameter of 9 _ 5 mi inches. Find its circumference WHEELS A hamster wheel has a radius of 4 _ 30 _ 4 in. inches. How far will the wheel turn in one revolution? 8 _ in. 0. PATCHES A National Guard military patch has a diameter of.5 inches. What is its circumference to the nearest tenth?.9 in. ft.6 cm 44 yd 66 ft. POOLS The Cole family owns an aboveground circular swimming pool that has walls made of aluminum. Find the length l of aluminum surrounding the pool as shown if the radius is 5 feet. Round to the nearest tenth. 94. ft l 586 Chapter Measurement: Two and ThreeDimensional Figures
4 LABELS Determine the length of each can s label cm 4..5 in. 54 in. _ 6 in..0 in. 3.4 cm MEASUREMENT For Exercises 5 8, perform each of the following steps See students work. $ " a. Use a centimeter ruler to measure the diameter of each circular object listed. b. Estimate to find the approximate circumference of each circle. $ " $ " c. Calculate the circumference of each circle. Use 3.4 for π. d. Cut a piece of string the length of the circumference of each circle. Use a centimeter ruler to measure the length of the string to the nearest tenth of a centimeter. Compare this actual length to the calculated length. RealWorld Link The record for the longest unicycle ride is 9,6 miles. Source: Guinness World Records 5. soup can lid 6. quarter. CD or DVD 8. button ALGEBRA Find the diameter or radius of each circle. Use 3.4 for π. Round to the 9. C = 5 ft, diameter = 3. C = 30 yd, radius = ft 8.0 ft yd 4.8 yd 30. C = 54 cm, diameter = 3. C = 48 km, radius = cm. cm km.6 km 33. UNICYCLES A unicycle wheel has a radius of 0 inches. How many feet will the unicycle travel in 5 revolutions? Explain how you solved this problem. See margin. 34. ROUNDABOUTS A roundabout is a oneway circular intersection. About how many feet would a car travel if it drove once around the roundabout? about 4 ft GU 35. FIND THE DATA Refer to the Data File on EXTRA PRACTICE See pages 69, 4. H.O.T. Problems 3. Elsa; Logan incorrectly applied the formula that uses the diameter. pages 6 9. Choose some data and write a realworld problem in which you would find the circumference of a circle. See students work. 36. OPEN ENDED Select a realworld situation in which finding the circumference of a circle would be useful. WA0A Sample answer: sewing fringe on a circular tablecloth 3. FIND THE ERROR Logan and Elsa are finding the circumference of a circle with a radius of inches. Who is correct? Explain. C = π or π C = π or 4π Logan Elsa Lesson 3 Circles and Circumference 58_CH_L3_84046.indd NETS Glencoe G SE MS Math _0588_CH_L3_84046 rw 00 Edit rw th pp 58 /8/09 :8:8 PM
5 CHALLENGE For Exercises 38 and 39, use the circle at the right. 38. How many lengths x will fit on the circle s circumference? 39. If the value of x is doubled, what effect will this have on the diameter? on the circumference? Explain your reasoning. x WRITING IN 40. MATH A constant is a quantity whose value never changes. In the formula for the circumference of a circle, identify any constants. Justify your response. 4. Malik s bike tire has a radius of 8 inches. Which equation could be used to find the circumference of the tire in inches? A C = π 4 C C = π 6 B C = π 6 D C = π Which measure is closest to the circumference of the dreamcatcher shown below? 5 in. 4. Each wheel on Nina s car has a diameter of 8 inches. Which expression could be used to find the circumference of the wheel? F 9 π H 9 9 π G 8 π J 8 8 π A.9 in. B 5. in. C 34. in. D 6.8 in. MEASUREMENT Find the area of each figure. Round to the nearest tenth if necessary. (Lesson ) ft 9.8 km. ft 5.0 km 3.8 ft 46. MEASUREMENT Find the area of a parallelogram with base 6.5 meters and height.0 meters. (Lesson ) 4. PROBABILITY Jorge rolled a number cube several times and recorded the results in the table shown. Find the experimental probability that an odd number turned up. (Lesson 9) PREREQUISITE SKILL Use a calculator to find each product to the nearest tenth. (Lesson 4) Outcome Frequency π π 50. π (.4) 5. π (4.5) 588 Chapter Measurement: Two and ThreeDimensional Figures
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