12-1 Circles and Circumference
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1 Find the circumference of each circle. Round to the nearest tenth. 1. Find the circumference of each circle. Round to the nearest tenth in m ft cm 50.9 cm 4. diameter = 10.5 centimeters 33.0 cm 5. radius = 3.6 kilometers 22.6 km 6. An ancient timber circle discovered in the United Kingdom was thought to have been built more than 4000 years ago. Known as Seahenge, this ancient circle has a circumference of about 21.3 meters. What is the radius of the circle to the nearest tenth? 3.4 m ft 50.3 in cm esolutions Manual - Powered by Cognero Page 1
2 km 13. diameter = 9.4 meters 29.5 m 14. radius = 13.7 millimeters 86.1 mm 15. radius = feet 70.7 ft 16. diameter = yards 45.9 yd 17. Compare the circumferences of the two sand dollars shown. Sample answer: Small sand dollar: C 3.9 in., large sand dollar: C 7.9 in.; the circumference of the small sand dollar is half the circumference of the large sand dollar. 18. The circumference of the Moon is about 6790 miles. What is the distance to the center of the Moon in kilometers? Round to the nearest kilometer. (Hint: 1 mile 1.6 kilometers) 1729 km 19. The tower at Philadelphia City Hall contains four clocks that have a radius of about 3.96 meters. Find how far the minute hand travels after each number of rotations around the clock face. Round to the nearest hundredth. a. 2 rotations b. rotation c. rotations a m b m c m 20. The world s largest carousel in Spring Green, Wisconsin, has a diameter of 80 feet. How far does a rider travel on an outside horse after 10 revolutions? Round to the nearest foot ft 21. A circular fountain at a park has a radius of 4 feet. The mayor wants to build a fountain that is quadruple the size of the current fountain. Find the circumference of the new fountain. Round to the nearest tenth ft 22. The world s largest rideable motorcycle travels one mile after about rotations of a tire. a. To the nearest tenth, how many feet does the motorcycle travel after one rotation of a tire? What does this measure represent? (Hint: 1 mile = 5280 feet) b. To the nearest tenth, how many feet tall are the tires? a ft; the circumference of the tire b. 6.2 ft esolutions Manual - Powered by Cognero Page 2
3 23. Multiple Representations In this problem, you will investigate the relationship between the radius and circumference of a circle. a. Table Make a table of values like the one shown. Find the circumference of a circle having each radius. Round to the nearest tenth. b. Graph Use your table to graph the circumference C of a circle as a function of the radius r. c. Analyze Describe the slope of the graph. How is the slope related to the formula for finding circumference? a. 24. The Beaverhead Crater is a large impact crater in the United States. If the circumference of the crater is about kilometers, what is the diameter of the crater? 60 km 25. Model with Mathematics Find a circular object in your home. Measure the diameter and use that value to calculate the circumference. Use a tape measure to check your calculation. Sample answer: A glass with a diameter of 7 centimeters has a circumference of about 22.0 centimeters. 26. Reason Abstractly A variable is a quantity with a value that changes. In the formula for the circumference of a circle, identify any variables. Both C and d. 27. Persevere with Problems Three congruent circles are inside a rectangle as shown. Which is greater, the length of the rectangle l, or the circumference of one circle? Explain your reasoning. b. Sample answer: c. 2π; Since the formula for the circumference of a circle, C = 2πr, is in the form of y = mx, 2π is the slope. Circumference of one circle; l equals 3d and the circumference of one circle is approximately 3.14d. 28. Justify Conclusions Explain why the formula C = πd can be used to calculate the length of a circular bracelet. If the bracelet is opened up and laid out flat, can the same formula be used to find the length? Explain. As a circle, the bracelet has a diameter. So, its length is the circumference of the circle. When the bracelet is laid out flat, it has no diameter. So, the formula for the circumference of a circle cannot be used. esolutions Manual - Powered by Cognero Page 3
4 29. Building on the Essential Question Describe the relationship between circumference and radius. How does the circumference change if the radius is increased? How does the radius change if the circumference is decreased? Circumference is 2π or about 6.3 times the radius. The circumference increases as the radius increases. The radius decreases as the circumference decreases. 30. A plate has a radius of 5 inches. Which equation could be used to find the circumference of the plate in inches? A C = 2(10π) B C = 5π C C = 10π D C = 2π C 31. A bicycle tire has a diameter of 24 inches. Find the circumference of the tire to the nearest tenth of an inch. F 75.4 in. G 83.5 in. H 87.9 in. J 91.5 in. F 32. A planter has a circumference of 37.6 inches. Which measure is closest to the diameter of the planter? A 10 in. B 11 in. C 12 in. D 14 in. C 33. Short Response The circle shown below has a diameter of 15 feet. What is the circumference to the nearest foot? 47 ft Find the area of each figure described. 34. parallelogram: base, 10 yd; height 5 yd 50 yd trapezoid: height 3 ft; bases, 15 ft and 20 ft 52.5 ft right triangle: height, 6 centimeters; base, 5 centimeters 15 cm parallelogram: height, 9 inches; base, 10 inches 90 in 2 Find the sum of the measures of the interior angles of each polygon. 38. triangle hexagon pentagon 540 esolutions Manual - Powered by Cognero Page 4
5 41. For every order submitted, an online bookstore charges a $5 shipping fee plus a charge of $2 per pound on the weight of the items being shipped. The total shipping charges y can be represented by y = 2x + 5, where x represents the weight of the order in pounds. Graph the equation c 7 > 5c + 14 c < It costs $15 per person to take a tour of an underground cave. a. Write an equation to determine the total cost for any number of people to take the tour. b. What is the total cost if 12 people take the tour? a. c = 15n b. $180 Solve each inequality. 42. b 14 > 23 b > n n p > x x m > 14 m < 2 esolutions Manual - Powered by Cognero Page 5
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