107: areas of circles, sectors, and...
TRANSCRIPT
![Page 1: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/1.jpg)
10.7 Areas of Circles Sectors and Segments
1
April 23, 2010
Apr 2012:26 PM
107: Areas of Circles, Sectors, and Segments.
Objective: Find the area of circles, sectors, and segments.
![Page 2: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/2.jpg)
10.7 Areas of Circles Sectors and Segments
2
April 23, 2010
Apr 2012:28 PM
Warmup
In one revolution, how much further does a 29 in. mountain bike tire travel than a 26 in. mountain bike tire? (tires are measured by their diameter).
1.
2. Over 1000 ft, how many more revolutions would the 26 in. tire make than the 29 in tire.
![Page 3: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/3.jpg)
10.7 Areas of Circles Sectors and Segments
3
April 23, 2010
Apr 202:29 PM
RefresherHow do you find the circumference of a circle?
How do you find the area of a circle?
![Page 4: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/4.jpg)
10.7 Areas of Circles Sectors and Segments
4
April 23, 2010
Apr 202:32 PM
New Vocabulary: SECTOR
A sector is a region bounded by two radii of a circle.
O
X
Y
The blue shaded region is called sector XOY.
How can we find the area of a sector if we know the measure of XOY ?
![Page 5: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/5.jpg)
10.7 Areas of Circles Sectors and Segments
5
April 23, 2010
Apr 217:32 AM
![Page 6: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/6.jpg)
10.7 Areas of Circles Sectors and Segments
6
April 23, 2010
Apr 217:37 AM
Find the area of sector ZOM.
A circle has a diameter of 20 cm. What is the area of a sector bounded by a 208o major arc?
![Page 7: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/7.jpg)
10.7 Areas of Circles Sectors and Segments
7
April 23, 2010
Apr 217:45 AM
Segment of a circle.
New Vocabulary: SEGMENT
A part of a circle bounded by an arc and the segment joining its endpoints is a segment of a circle.
![Page 8: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/8.jpg)
10.7 Areas of Circles Sectors and Segments
8
April 23, 2010
Apr 217:51 AM
O
A
B
How do we find the area of segment AB given the measure of AOB and the radius ?
![Page 9: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/9.jpg)
10.7 Areas of Circles Sectors and Segments
9
April 23, 2010
Apr 217:56 AM
Area of a segment
![Page 10: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/10.jpg)
10.7 Areas of Circles Sectors and Segments
10
April 23, 2010
Apr 217:59 AM
Find the area of segment AB.
![Page 11: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/11.jpg)
10.7 Areas of Circles Sectors and Segments
11
April 23, 2010
Apr 218:01 AM
A circle has a radius of 12 cm. Find the area of the smaller segment of the circle bounded by a 60o arc.
Practice
![Page 12: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/12.jpg)
10.7 Areas of Circles Sectors and Segments
12
April 23, 2010
Apr 218:04 AM
Challenge Problem
10 ft
8 ft
![Page 13: 107: Areas of Circles, Sectors, and Segments.staffweb.psdschools.org/kemotich/Mrs_Motichka/Geometry/Chapter 10... · 10.7 Areas of Circles Sectors and Segments 1 April 23, 2010 Apr](https://reader034.vdocument.in/reader034/viewer/2022050807/5a9e38d97f8b9a2e688c323a/html5/thumbnails/13.jpg)
10.7 Areas of Circles Sectors and Segments
13
April 23, 2010
Apr 218:15 AM
Homework
p. 578 #7 19 odd, 22 27