10.1 circles and circumference 2017 ink.notebook. March 13, Page 91. Page 92. Page 90. Ch 10 Circles Circles and Circumference.
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1 Page 90 Page 91 Page 92 Ch 10 Circles 10.1 Circles and Circumference Lesson Objectives Page 93 Standards Lesson Notes Page Circles and Circumference Press the tabs to view details. 1
2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes After this lesson, you should be able to successfully identify and use parts of circles. You should also be able to find the circumference of a circle. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Press the tabs to view details. Circle Set of all points in a plane equidistant from a fixed point Chord A segment whose endpoints lie on the circle G F Radius A Segment whose endpoints are the center of a circle and a point on the circle Diameter Any chord that contains the center of the circle H E D C L J K Secant A line that contains a chord Tangent A line in a plane of a circle that intersects the circle in EXACTLY one point A circle consists of all points in a plane that are a given distance, called the radius, from a given point called the center. A segment or line can intersect a circle in several ways. A segment with endpoints that are at the center and on the circle is a. A segment with endpoints on the circle is a. A chord that passes through the circle's center and made up of collinear radii is a. 2
3 Radius Diameter d = 2r r =1 2d EXAMPLE Name the circle: A B E F Name all the: Chords: Radii: D C Diameters: The circumference of a circle is the distance around the circle. For a circumference of C units and a diameter of d units or a radius or r units, C = 2¹ r STOP! C = d¹ Use 3.14 for ¹ 1. Find the circumference of the circle to the nearest hundredth. 13 cm 3
4 Finding the diameter and radius from the circumference: 1) 2) 3) 4) Divide circumference by 3.14 Your answer is the diameter Divide the diameter by 2 Your answer is the radius Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. 2. C = 40 in When finding the exact circumference, do NOT type pi or 3.14 into the calculator. Your answer will be in terms of pi, for instance 5¹. Find the exact circumference of each circle using the given inscribed or circumscribed polygon cm 11 yd 12 cm 4
5 1. Name the circle. 2. Name radii of the circle. O A 3. Name chords of the circle C B D 4. Name the circle. A X 5. Name radii of the circle. 6. Name chords of the circle. 7. Name diameters of the circle. R Y B 8. If AB = 18 mm, find AR. 5
6 9. If RY = 10 in, find AR and AB. A X R Y B Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. 11. C = 256 ft 12. C = m 6
7 Find the exact circumference of each circle using the given inscribed or circumscribed polygon. Find the exact circumference of each circle using the given inscribed or circumscribed polygon cm 3 mm 7 mm 6 cm 9 in 16. WHEELS Zack is designing wheels for a concept car. The diameter of the wheel is 18 inches. Zack wants to make spokes in the wheel that run from the center of the wheel to the rim. In other words, each spoke is a radius of the wheel. How long are these spokes? 7
8 17. SEWING Ms. Singer is going to put lace around the edge of the round tablecloth she just finished making. If the tablecloth has a diameter of 12 ft. How much lace will she need? 18. CAKE CUTTING Kathy slices through a circular cake. The cake has a diameter of 14 inches. The slice that Kathy made is straight and has a length of 11 inches. Did Kathy cut along a radius, a diameter, or a chord of the circle? On the Worksheet 8
9 HOMEWORK 10.1 Practice WS on Circles and Circumference For Exercises 1 7, refer to ÀP. 1. Name the circle. 2. Name a radius. 3. Name a chord. 4. Name a diameter. 5. Name a radius not drawn as part of a diameter. 6. Suppose the diameter of the circle is 16 cm. Find the radius. C A D P B E 7. If PC = 11 in, find AB. The diameters of ÀF and ÀG are 5 and 6 units, respectively. Find each measure. Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. 10. C = 36 m 11. C = 17.2 ft 12. C = 5 yd 8. BF 9. AB 9
10 Find the exact circumference of each circle using the given inscribed or circumscribed polygon Find the exact circumference of each circle using the given inscribed or circumscribed polygon Find the exact circumference of each circle using the given inscribed or circumscribed polygon SUNDIALS Herman purchased a sundial to use as the centerpiece for a garden. The diameter of the sundial is 9.5 inches. a) Find the radius of the sundial. b) Find the circumference of the sundial to the nearest hundredth. 10
11 20. COINS Three identical circular coins are lined up in a row as shown. The distance between the centers of the first and third coins is 3.2 centimeters. What is the radius of one of these coins? 21. PLAZAS A rectangular plaza has a surrounding circular fence. The diagonals of the rectangle pass from one point on the fence through the center of the circle to another point on the fence. Based on the information in the figure, what is the diameter of the fence? Round your answer to the nearest tenth of a foot. 22. EXERCISE HOOPS Taiga wants to make a circular loop that he can twirl around his body for exercise. He will use a tube that is 2.5 meters long. a) What will be the diameter of Taiga's exercise hoop? Round your answer to the nearest thousandth of a meter. Answers: b) What will be the radius of Taiga's exercise hoop? Round your answer to the nearest thousandth of a meter. 11
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