-4 Aea of Cicles MAIN IDEA Find the aeas of cicles. Fold a pape plate in half fou times to New Vocabulay Label the adius as shown. Let C secto Math Online glencoe.com Exta Examples Pesonal Tuto Self-Check Quiz divide it into 6 equal-sized sections. C epesent the cicumfeence of the cicle. Cut out each section; eassemble to fom a paallelogam-shaped figue.. What is the measuement of the base and the height? C ; (height). Substitute these values into C (base) the fomula fo the aea of a paallelogam. A = C ( ) 3. Replace C with the expession fo the cicumfeence of a cicle, π. Simplify the equation and descibe what it epesents. 3. A = (π) (); A = π ; the aea of a cicle In the Mini Lab, the fomula fo the aea of a paallelogam was used to develop a fomula fo the aea of a cicle. Aea of a Cicle Wods Key Concept The aea A of a cicle equals the poduct of π and the squae of its adius. Symbols Model A = π Find the Aea of a Cicle Find the aea of the cicle. A = π Aea of a cicle A = π Replace with. [π] in..5663706 The aea of the cicle is appoximately.6 squae inches. a. Find the aea of a cicle with a adius of 3. centimetes. Round to the neaest tenth. 3. cm Lesson -4 Aea of Cicles 58905890593CHL4874046 589 589 9/6/07 7:34:46 PM
COINS Find the aea of the face of the Wisconsin quate shown. The diamete of the quate is 4 millimetes, 4 mm so the adius is ( 4) o millimetes. A = π Aea of a cicle A = π Replace with. A 45.4 Use a calculato. The aea is appoximately 45.4 squae millimetes. b. POOLS The bottom of a cicula swimming pool with diamete 30 feet is painted blue. How many squae feet ae blue? 706.5 ft Radii The plual fom of adius is adii. A secto of a cicle is a egion of a cicle bounded by two adii. 3 Ellis daws a cicle with a diamete of 6 inches, and shades one egion of the cicle. Find the appoximate aea of the secto. A 00 in C 40 in B 0 in D 804 in 6 in. 80 Identifying What is Given Befoe finding aea, be sue to ead the question caefully and identify if the adius o diamete is given. Read the Item The diamete of the cicle is 6 inches. Since thee ae 360 in a cicle, the secto is 80 360 o the aea of the entie cicle. Solve the Item A = π Aea of a cicle A = π 8 Replace with 6 o 8. A 00 Multiply. Use 3.4 fo π. The aea of the secto is appoximately (00) o 00 squae inches. The answe is A. c. Ray dew one cicle with a adius of 7 centimetes and anothe cicle with a adius of 0 centimetes. Find the appoximate diffeence between the aeas of the cicles. H F 8 cm G 40 cm H 60 cm J 54 cm 590 Chapte Measuement: Two- and Thee-Dimensional Figues
indicates multi-step poblem Examples, (pp. 589 590) Find the aea of each cicle. Round to the neaest tenth. 0. m. 78.5 cm 54.5. 54.5 in 3. diamete = 6 m 5 cm 9 in. 4. diamete = 3 ft 3.7 ft Example 3 (p. 590) 5. MULTIPLE CHOICE Kenneth daws the cicle shown at the ight. He shades one egion of the cicle. What is the appoximate aea of the secto? B A 88 yd C 30 yd B 54 yd D 65 yd Answes wee computed using the π key on a calculato. 4 yd HOMEWORK HELP Fo Execises 6 7, 0, 4 5, 9 8 9, 3, 6 8 36 38 See Examples 3 Execise Levels A: 6 9 B: 0 9 C: 30 35 HELP Find the aea of each cicle. Round to the neaest tenth. 6. 0. cm 7. 8.3 in 8. 95.0 ft 9. 7 cm 8 cm 3 in. ft 7.0 cm 0. 8. m. 3. mm.4 m 3. mm. diamete = 8.4 m 3. diamete =.6 cm 4. adius = 4 in. 63.6 in 55.4 m 5. adius = 3 3 4.7 cm 4 ft 6. diamete = 9 4 mi 7. diamete = 0 3 4 yd 44. ft 67. mi 338. yd 8. PATCHES Find the aea of the Gil Scout patch shown if the diamete is.5 inches. Round to the neaest tenth.. in 9. TOOLS A spinkle that spays wate in a cicula aea can be adjusted to spay up to 30 feet. To the neaest tenth, what is the maximum aea of lawn that can be wateed by the spinkle?,87.4 ft ESTIMATION Estimate to find the appoximate aea of each cicle. 0. Sample. Sample. 8 cm answe: 5.9 ft answe: 3.8 in. 3 4 = 3 6 = 48 cm 08 ft Sample answe: 3 7 = 47 in Lesson -4 Aea of Cicles 59
PRACTICE EXTRA PRACTICE See pages 698, 74. Fo Execises 3 6, use a compass to daw the cicle shown on centimete gid pape. 3. Count the numbe of squaes that lie completely within the cicle. Then count the numbe of squaes that lie completely within o contain the cicle. 4. Estimate the aea of the cicle by finding the mean of the two values you found in Execise 3. 5. Find the aea of the cicle by using the aea fomula. 6. How do the aeas you found in Execises 4 and 5 compae to one anothe? 7. A semicicle is half a cicle. Find the aea of the semicicle to the neaest tenth. 8. Which has a geate aea, a tiangle with a base 8.6 m of 00 feet and a height of 00 feet o a cicle with diamete of 00 feet? Justify you selection. 9. RADIO SIGNALS A adio station sends a signal in a cicula aea with an 80- mile adius. Find the appoximate aea in squae kilometes that eceives the signal. (Hint: squae mile.6 squae kilometes) H.O.T. Poblems 30. REASONING If the length of the adius of a cicle is tipled, does the aea also tiple? Explain you easoning. 4 ft ft CHALLENGE Find the aea of the shaded egion in each figue. Round to the neaest tenth. 3. 3. 33. 8 m 3.5 cm m 5.5 in..5 cm 34. FIND THE ERROR Dasan and Camen ae finding the aea of a cicle that has a diamete of 6 centimetes. Who is coect? Explain. A = π (6) 804 cm A = π (8) 0 cm WRITING IN Dasan Camen 35. MATH Wite and solve a eal-wold poblem in which you would solve the poblem by finding the aea of a cicle. 59 Chapte Measuement: Two- and Thee-Dimensional Figues
36. The adius of the half dolla in centimetes is given below. Find the appoximate aea of the shaded secto. A.95 cm 38. Which two figues have the same aea shaded? A m 8 m 7.5 m m Figue I Figue II 0 m A 6 cm C 4 cm B cm D 8 cm 37. Which equation could be used to find the aea in squae inches of a cicle with a adius of inches? J F A = 6 π H A = π G A = π 6 J A = π m m 80 6 m Figue III Figue IV A Figue I and Figue IV B Figue I and Figue II C Figue II and Figue IV D Figue II and Figue III 39. MEASUREMENT What is the cicumfeence of a cicle that has a adius of 8 yads? Use 3.4 fo π and ound to the neaest tenth if necessay. (Lesson -3) 50. yd 40. MEASUREMENT Find the aea of a tiangle with a base of metes and a height of 7 metes. (Lesson -) 83.5 m Find the aea of each paallelogam. Round to the neaest tenth if necessay. (Lesson -) 4. 0 in. in. 0 in 4. 5 cm 7.9 cm 39.5 cm 43. 00. m 8.7 m.5 m PREREQUISITE SKILL Simplify each expession. (Lessons -, -3, and -4) 44. 8. 5 7.5 45. 3.4 6 3.04 46. 5.4 + 5.58 47. 7 + (9)(4) 50.5 Lesson -4 Aea of Cicles 593