Circumference of a Circle BEFORE Now WHY? You found the perimeters You’ll find the circumferences So you can find the distance around of polygons. of circles. a Ferris wheel, as in Ex. 20. Acircle is the set of all points in a center Word Watch plane that are the same distance from radius a fixed point called thecenter . The circle, p. 563 diameter center, p. 563 distance from the center to any point radius, p. 563 on the circle is the radius . The distance diameter, p. 563 across the circle through the center is circumference circumference, p. 563 thediameter . Thecircumference of a circle is the d distance around the circle. The ratio of a circle’s circumference to its diameter d is represented by the Greek letter (pi). diameter d From the figure, you can see that is slightly greater than 3. The values 3.14 d 22 and ᎏᎏ are often used as approximations 7 of the number , which is a nonterminating, nonrepeating decimal: 3.14159. Circumference of a Circle Words The circumference C of a circle diameter d is the product of and the diameter, or twice the product of and the radius. radius r Algebra C ϭ dCϭ 2 r EXAMPLE 1 Finding the Circumference of a Circle Find the circumference of the clock. Use 3.14 for . atch Out W ! C ϭ d Write formula for circumference. 25 cm ≈ 3.14(25) Substitute 3.14 for and 25 for d. The circumference ϭ Multiply. of a circle is measured in 78.5 linear units, not square units. ANSWER The circumference of the circle is about 78.5 centimeters. Lesson 11.6 Circumference of a Circle 563 EXAMPLE 2 Finding the Circumference of a Circle 22 with Find the circumference of the circle. Use ᎏᎏ for . Solving 7 21 in. When the radius or C ϭ 2 r Write formula for circumference. diameter of a circle is 22 22 22 divisible by 7, use ᎏᎏ ≈ 2 ᎏᎏ (21) Substitute ᎏᎏ for and 21 for r. 7 ΂ 7 ΃ 7 as the approximation for . ϭ 132 Multiply. ANSWER The circumference of the circle is about 132 inches. 22 Your turn now Find the circumference of the circle. Use ᎏᎏ or 7 3.14 for . 1. 2. 3. 100 cm 49 in. 9 mm EXAMPLE 3 Finding the Diameter of a Circle Nature Giant Sequoias The largest tree in the United States is growing in Sequoia National Park in California. The tree is a giant sequoia whose trunk is roughly circular and has a circumference of 998 inches. What is the tree’s diameter? Solution C ϭ d Write formula for circumference. 998 ≈ 3.14d Substitute 998 for C and 3.14 for . 998 3.14d ᎏᎏ ≈ ᎏᎏ Divide each side by 3.14. 3.14 3.14 318 ≈ d Simplify. I Giant Sequoias ANSWER The largest tree in the United The tree’s diameter is about 318 inches. States is 275 feet tall. About how many times taller is the tree than a person who is 5 foot 9 inches tall? Your turn now Solve the following problem. 4. The circumference of a circle is 22 inches. Find the circle’s diameter. Round your answer to the nearest whole number. 564 Chapter 11 Measurement and Area INTERNET Exercises eWorkbook Plus More Practice, p. 715 CLASSZONE.COM Getting Ready to Practice 1. Vocabulary Label a circle’s diameter, center, radius, and circumference. Match the radius or diameter of a circle with the circle’s circumference. 2. r ϭ 4 cm 3. d ϭ 2 cm 4. r ϭ 2 cm A. C ϭ 2cm B. C ϭ 4cm C. C ϭ 8cm 5. Find the Error Describe and correct C ϭ d the error in finding the circumference ≈ 3.14(5) of a circle with a radius of 5 meters. ϭ 15.7 m 6. Monocycle A giant monocycle wheel has a diameter of 7 feet. 22 What is the circumference of the wheel? Use ᎏᎏ for . 7 Practice and Problem Solving 22 Find the circumference of the circle. Use ᎏᎏ or 3.14 for . 7 7. d ϭ 9 in. 8. d ϭ 30 in. 9. d ϭ 6.5 cm 10. r ϭ 3.4 in. 11. d ϭ 1.205 in. 12. r ϭ 14 cm with Homework Example Exercises 1 7–12 Find the diameter and the radius of the circle with the given 22 2 7–12 circumference. Use ᎏᎏ or 3.14 for . 7 3 13–18 13. C ϭ 28.26 in. 14. C ϭ 119.32 m 15. C ϭ 81.64 mm Online Resources 3 CLASSZONE.COM 16. C 42.39 km 17. C 39 ᎏᎏ cm 18. C 19.468 ft 5 • More Examples • eTutorial Plus 19. Writing If you triple the diameter of a circle, what happens to the circle’s circumference? Give an example to support your conclusion. Lesson 11.6 Circumference of a Circle 565 20. Ferris Wheel The original Ferris wheel, designed by George Ferris in 1892 for the World’s Columbian Exposition in Chicago, had a radius of 125 feet. What was the circumference of the original Ferris wheel? 21. Critical Thinking What is the circumference of the largest circle that can fit inside a square with 5 in. a side length of 5 inches? 22. Compare To 9 decimal places, the number is 3.141592654. To how 22 many decimal places is ᎏᎏ an accurate approximation of ? 7 23. Challenge How fast does the tip of a 5 inch minute hand on a clock travel? How fast does the tip of a 6 inch second hand on a clock travel? Express your answers in inches per hour. Mixed Review Use a proportion to answer the question. (Lesson 9.2) 24. What percent of 180 is 81? 25. What percent of 90 is 36? Choose a Strategy Use a strategy from Problem Solving Strategies the list at the right to solve the following problem. Explain your choice of strategy. I Make a List I Break into Parts I Write an Equation 26. You joined a summer reading group. You’ve read 2 books: 194 pages and 212 pages. Your goal is to read 1000 pages by the end of August. If there are 45 days until the end of August, what is the mean number of pages you must read each day in order to reach your goal? Basic Skills Copy and complete the statement. 27. 45 mi ϭ _?_ ft 28. 54 oz ϭ _?_ lb _?_ oz Test-Taking Practice INTERNET 29. Multiple Choice The Astrodome in Houston, Texas, is circular and has State Test Practice a diameter of 710 feet. What is the approximate circumference of the CLASSZONE.COM Astrodome? A. 1110 ft B. 2230 ft C. 4460 ft D. 15,600 ft 30. Multiple Choice A circular wading pool has a diameter of 4 feet. A circular swimming pool has a radius of 16 feet. How many times larger is the circumference of the swimming pool than the wading pool? F. 2 times G. 4 times H. 8 times I. 12 times 566 Chapter 11 Measurement and Area.