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FeatureLesson Geometry Lesson Main 1. A circle graph has a section marked Potatoes: 28%. What is the measure of the central angle of this section? 2. Explain.

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Presentation on theme: "FeatureLesson Geometry Lesson Main 1. A circle graph has a section marked Potatoes: 28%. What is the measure of the central angle of this section? 2. Explain."— Presentation transcript:

1 FeatureLesson Geometry Lesson Main 1. A circle graph has a section marked Potatoes: 28%. What is the measure of the central angle of this section? 2. Explain how a major arc differs from a minor arc. Use O for Exercises 3–6. 3. Find mYW. 4. Find mWXS. 5. Suppose that P has a diameter 2 in. greater than the diameter of O. How much greater is its circumference? Leave your answer in terms of. 6. Find the length of XY. Leave your answer in terms of.... A major arc is greater than a semicircle. A minor arc is smaller than a semicircle Lesson 10-6 Circles and Arcs Lesson Quiz 10-7

2 FeatureLesson Geometry Lesson Main (For help, go to Lesson 10-6.) 1. What is the radius of a circle with diameter 9 cm? 2. What is the diameter of a circle with radius 8 ft? 3. Find the circumference of a circle with diameter 12 in. 4. Find the circumference of a circle with radius 3 m. Lesson 10-7 Areas of Circles and Sectors Check Skills Youll Need 10-7 The radius is half the diameter: 9 ÷ 2 = 4.5 cm The diameter is twice the radius: (8)(2) = 16 ft C = d = (12) = 12, or about 37.7 in. C = 2 r = 2 (3) = 6, or about 18.8 m 5. Suppose that circle P has a diameter 2 in. greater than the diameter of circle O. How much greater is its circumference? Leave your answer in terms of. 6. Find the length of XY. Leave your answer in terms of. 2 9

3 FeatureLesson Geometry Lesson Main

4 FeatureLesson Geometry Lesson Main

5 FeatureLesson Geometry Lesson Main Lesson 10-7 Areas of Circles and Sectors Notes 10-7

6 FeatureLesson Geometry Lesson Main Lesson 10-7 Areas of Circles and Sectors Notes 10-7 A sector of a circle is a region bounded by an arc of the circle and the two radii to the arcs endpoints. You name a sector using one arc endpoint, the center of the circle, and the other arc endpoint. The slice of pizza at the left is sector XOY of circle O.

7 FeatureLesson Geometry Lesson Main Lesson 10-7 Areas of Circles and Sectors Notes 10-7

8 FeatureLesson Geometry Lesson Main Lesson 10-7 Areas of Circles and Sectors Notes 10-7 A part of a circle bounded by an arc and the segment joining its endpoints is a segment of a circle.

9 FeatureLesson Geometry Lesson Main Lesson 10-7 Areas of Circles and Sectors Notes 10-7 To find the area of a segment for a minor arc, draw radii to form a sector. The area of the segment equals the area of the sector minus the area of the triangle formed.

10 FeatureLesson Geometry Lesson Main Because the diameters are in different units, convert 1 ft to 12 in. The radius of the archery target is 1 ft = 12 in. The area of the archery target is r 2 = (12) 2 = 144 in. 2 A circular archery target has a 2-ft diameter. It is yellow except for a red bulls-eye at the center with a 6-in. diameter. Find the area of the yellow region. Round your answer to the nearest whole number. Find the areas of the archery target and the bulls-eye. The radius of the archery target is = 1 ft Lesson 10-7 Areas of Circles and Sectors Additional Examples 10-7 Real-World Connection

11 FeatureLesson Geometry Lesson Main The area of the red region is r 2 = (3) 2 = 9 in. 2 The radius of the red region is = 3 in (continued) Use a calculator The area of the yellow region is about 424 in. 2 area of archery target – area of red region = area of yellow region 144 –9 =135 Lesson 10-7 Areas of Circles and Sectors Quick Check Additional Examples 10-7

12 FeatureLesson Geometry Lesson Main The area of sector ACB is 10 m 2. = 10 = = (6) Find the area of sector ACB. Leave your answer in terms of. area of sector ACB = r 2 mAB 360 Lesson 10-7 Areas of Circles and Sectors Quick Check Additional Examples 10-7 Finding the Area of a Sector of a Circle

13 FeatureLesson Geometry Lesson Main = (24) 2 Substitute = 576 = 192 Simplify area of sector AOB = r 2 Use the formula for area of a sector. mAB 360 Lesson 10-7 Areas of Circles and Sectors Find the area of the shaded segment. Round your answer to the nearest tenth. Step 1: Find the area of sector AOB. Additional Examples 10-7 Finding the Area of a Segment of a Circle.

14 FeatureLesson Geometry Lesson Main A = bhArea of a triangle A = (24 3 )(12)Substitute 24 for b and 12 for h. A = 144 3Simplify You can use a 30°-60°-90° triangle to find the height h of AOB and AB. 24 = 2hhypotenuse = 2 shorter leg 12 = hDivide each side by 2. = 3 12 = 12 3longer leg = 3 shorter leg AB = 24 3Multiply each side by 2. AB 2 (continued) Step 2: Find the area of AOB. AOB has base 12 3 ft ft, or 24 3 ft and height 12 ft. Lesson 10-7 Areas of Circles and Sectors Additional Examples 10-7

15 FeatureLesson Geometry Lesson Main area of segment = 192 – To the nearest tenth, the area of the shaded segment is ft Use a calculator. Step 3: Subtract the area of AOB from the area of sector AOB to find the area of the segment of the circle. (continued) Lesson 10-7 Areas of Circles and Sectors Quick Check Additional Examples 10-7

16 FeatureLesson Geometry Lesson Main 1. A park contains two circular playgrounds. One has a diameter of 60 m, and the other has a diameter of 40 m. How much greater is the area of the larger playground? Round to the nearest whole number. 2. A circle has an 8-in. radius. Find the area of a sector whose arc measures 135. Leave your answer in terms of. For Exercises 3 and 4, find the area of the shaded segment. Round to the nearest whole unit m 2 24 in cm in. 2 Lesson 10-7 Areas of Circles and Sectors Lesson Quiz 10-7


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