featurelesson geometry lesson main 1. a circle graph has a section marked potatoes: 28%. what is the...
TRANSCRIPT
![Page 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/1.jpg)
FeatureLesson
GeometryGeometry
LessonMain
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.
100.8
270
30
2
9
Lesson 10-6
Circles and ArcsCircles and Arcs
Lesson Quiz
10-7
![Page 2: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/2.jpg)
FeatureLesson
GeometryGeometry
LessonMain
(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 SectorsAreas of Circles and Sectors
Check Skills You’ll Need
Check Skills You’ll 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 = 2r = 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
![Page 3: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/3.jpg)
FeatureLesson
GeometryGeometry
LessonMain
![Page 4: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/4.jpg)
FeatureLesson
GeometryGeometry
LessonMain
![Page 5: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/5.jpg)
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Notes
10-7
![Page 6: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/6.jpg)
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-7
Areas of Circles and SectorsAreas 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 arc’s 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.
![Page 7: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/7.jpg)
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Notes
10-7
![Page 8: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/8.jpg)
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-7
Areas of Circles and SectorsAreas 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.
![Page 9: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/9.jpg)
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-7
Areas of Circles and SectorsAreas 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.
![Page 10: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/10.jpg)
FeatureLesson
GeometryGeometry
LessonMain
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 r2 = (12)2 = 144 in.2
A circular archery target has a 2-ft diameter. It is
yellow except for a red bull’s-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 bull’s-eye.
The radius of the archery target is = 1 ft.22
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Additional Examples
10-7
Real-World Connection
![Page 11: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/11.jpg)
FeatureLesson
GeometryGeometry
LessonMain
The area of the red region is r2 = (3)2 = 9 in.2
The radius of the red region is = 3 in.62
(continued)
Use a calculator. 135 424.11501
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 SectorsAreas of Circles and Sectors
Quick Check
Additional Examples
10-7
![Page 12: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/12.jpg)
FeatureLesson
GeometryGeometry
LessonMain
The area of sector ACB is 10 m2.
= 10
= • 36 5 18
= • (6)2100360
Find the area of sector ACB. Leave your answer in terms of .
area of sector ACB = • r 2mAB 360
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Quick Check
Additional Examples
10-7
Finding the Area of a Sector of a Circle
![Page 13: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/13.jpg)
FeatureLesson
GeometryGeometry
LessonMain
= • (24)2 Substitute.120360
= • 576 = 192 Simplify.13
area of sector AOB = • r2 Use the formula for area of a sector.
mAB 360
Lesson 10-7
Areas of Circles and SectorsAreas 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.
![Page 14: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/14.jpg)
FeatureLesson
GeometryGeometry
LessonMain
A = bh Area of a triangle
A = (24 3 )(12) Substitute 24 for b and 12 for h.
A = 144 3 Simplify.
1212
You can use a 30°-60°-90° triangle to find the height h of AOB and AB.
24 = 2h hypotenuse = 2 • shorter leg
12 = h Divide each side by 2.
= 3 • 12 = 12 3 longer leg = 3• shorter leg
AB = 24 3 Multiply each side by 2.
AB 2
(continued)
Step 2: Find the area of AOB.
AOB has base 12 3 ft + 12 3 ft, or 24 3 ft and height 12 ft.
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Additional Examples
10-7
![Page 15: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/15.jpg)
FeatureLesson
GeometryGeometry
LessonMain
area of segment = 192 – 144 3
To the nearest tenth, the area of the shaded segment is 353.8 ft2.
353.77047 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 SectorsAreas of Circles and Sectors
Quick Check
Additional Examples
10-7
![Page 16: 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](https://reader035.vdocuments.net/reader035/viewer/2022062404/5514dc8555034693478b554a/html5/thumbnails/16.jpg)
FeatureLesson
GeometryGeometry
LessonMain
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.3. 4.
1571 m2
24 in.2
15 cm2 138 in.2
Lesson 10-7
Areas of Circles and SectorsAreas of Circles and Sectors
Lesson Quiz
10-7