10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
10­7: Areas of Circles, Sectors, and Segments.
Objective: Find the area of circles, sectors, and segments.
Apr 20­12:26 PM
1
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Warm­up
1. 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).
2. Over 1000 ft, how many more revolutions would the 26 in. tire make than the 29 in tire.
Apr 20­12:28 PM
2
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Refresher
How do you find the circumference of a circle?
How do you find the area of a circle?
Apr 20­2:29 PM
3
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
New Vocabulary: SECTOR
A sector is a region bounded by two radii of a circle.
X
The blue shaded region is called sector XOY.
O
Y
How can we find the area of a sector if we know the measure of XOY ?
Apr 20­2:32 PM
4
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Apr 21­7:32 AM
5
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
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?
Apr 21­7:37 AM
6
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
New Vocabulary: SEGMENT
A part of a circle bounded by an arc and the segment joining its endpoints is a segment of a circle.
Segment of a circle.
Apr 21­7:45 AM
7
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
How do we find the area of segment AB given the measure of AOB and the radius ?
A
O
B
Apr 21­7:51 AM
8
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Area of a segment
Apr 21­7:56 AM
9
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Find the area of segment AB.
Apr 21­7:59 AM
10
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Practice
A circle has a radius of 12 cm. Find the area of the smaller segment of the circle bounded by a 60o arc.
Apr 21­8:01 AM
11
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Challenge Problem
8 ft
10 ft
Apr 21­8:04 AM
12
10.7 ­ Areas of Circles ­ Sectors and Segments
April 23, 2010
Homework
p. 578 #7 ­ 19 odd, 22 ­ 27
Apr 21­8:15 AM
13