confidential 1 geometry sector area and arc length
TRANSCRIPT
CONFIDENTIAL 1
GeometryGeometry
Sector Area Sector Area and Arc Lengthand Arc Length
CONFIDENTIAL 2
Warm UpWarm Up
Find the indicated measure.
(10x - 28)
(2x + 2)
LK
J
H
G
F
3) mJFH2) mKJ1) mKLJ
CONFIDENTIAL 3
Sector Area and arc lengthSector Area and arc length
The area of a circle is a fraction ofthe circle containing the sector.
To find the area of a sector whose central angle measures, multiply
the area of a circle by .mm
360
CONFIDENTIAL 4
Sector of a circleSector of a circle
TERM NAME DIAGRAM AREA
A sector of a circle is a region bounded by two radii
of the circle and their intercepted arc.
sector ACB
A =rm
360
CONFIDENTIAL 5
A) sector MPN
A = r2m
360 Use formula for area of sector
= (3)280
360 Substitute 3 for r and 80 for m
= 2 in 2 6.28 in 2 Simplify
Find the area of each sector. Give your answer in terms
of and rounded to the nearest hundredth.
3 in80
P
N
M
Finding the Area of the Sector
CONFIDENTIAL 6
B) sector EFG
A = r2m
360 Use formula for area of sector
= (6)2120
360 Substitute 6 for r and 120 for m
= 12 37.70 cm2 Simplify
G
F
E
6 cm120
CONFIDENTIAL 7
Now You Try!
Find the area of each sector. Give your answer in terms
of and rounded to the nearest hundredth.
1) sector ACB 2) sector JKL
CONFIDENTIAL 8
A circular plot with a 720 ft diameter is watered by a spray irrigation system. To the nearest square
foot, what is the area that is watered as the sprinkler rotates through an angle of 50 ?
A = r2m
360
= (360)250
360 d = 720 ft, r = 360 ft.
= 56.549 ft2 Simplify
CONFIDENTIAL 9
Now You Try!
2) To the nearest square foot, what is the area watered in previous example as the sprinkler
rotates through a semicircle ?
CONFIDENTIAL 10
A segment of a circle is a region bounded by an arc and its chord. The shaded region in the
figure is a segment
CONFIDENTIAL 11
Area of a segment
area of sectorarea of segment area of triangle
=
=
-
-
CONFIDENTIAL 12
Finding the Area of a SegmentFind the area of segment ACB to the nearest hundredth.
12 in
60BC
A
Step 1 Find the area of sector ACB.
A = r2m
360 Use formula for area of a sector
= (12)260
360 Substitute 12 for r and 60 for m
= 24 in2
CONFIDENTIAL 13
BC
A
Step 2 Find the area of ACB. Draw altitute AD.
A = 1
2 bh =
1
2(12) (6 3) CD = 6 in and h = (6 3) in
= 36 3 in2 simplify
Step 3 area of segment = areaof sector ACB - area of ACB = 24 36 3 =13.04 in2
CONFIDENTIAL 14
Now You Try!
3) Find the area of segment RST to the nearest hundredth.
CONFIDENTIAL 15
In the same way that the area of a sector is a fraction of the area of the
circle ,the length of an arc is a fraction of the circumference of the circle.
CONFIDENTIAL 16
Arc Length
TERM DIAGRAM LENGTH
Arc length is the distancealong an arc measured in linear
units. m
B
A
L = 2rm
360
CONFIDENTIAL 17
Finding Arc Length
Find each arc length. Give your answer in terms of and rounded to the nearest hundredth.
A) CD
L = 2rm
360 Use formula for arc length
= 2 (10)90
360 Substitute 10 for r and 90 for m
= 5 ft 15.71ft Simplify
90
10 ft
C
D
CONFIDENTIAL 18
B) an arc with measure 35 in a circle with radius 3 in.
L = 2rm
360 Use formula for arc length
= 2 (3)35
360 Substitute 3 for r and 35 for m
= 7
12in 1.83 in Simplify
CONFIDENTIAL 19
Now You Try!
Find each arc length. Give your answer in terms of and rounded to the nearest hundredth.
1) GH 2) an with measure 135 in a circle with radius 4 cm
6 m
H
G40
CONFIDENTIAL 20
Now some problems for you to practice.
CONFIDENTIAL 21
ASSESSMENT
Find the area of each segment to the nearest hundredth.
1)
CONFIDENTIAL 22
2)
CONFIDENTIAL 23
3)
CONFIDENTIAL 24
Find each arc length. Give your answer in terms of and rounded to the nearest hundredth.
4)
16 ft
FE 45
EF
CONFIDENTIAL 25
5)
9 m
120
Q
PQ
CONFIDENTIAL 26
Sector Area and arc lengthSector Area and arc length
The area of a circle is a fraction ofthe circle containing the sector.
To find the area of a sector whose central angle measures, multiply
the area of a circle by .mm
360
REVIEW
CONFIDENTIAL 27
Sector of a circleSector of a circle
TERM NAME DIAGRAM AREA
A sector of a circle is a region bounded by two radii
of the circle and their intercepted arc.
sector ACB
A =rm
360
CONFIDENTIAL 28
A) sector MPN
A = r2m
360 Use formula for area of sector
= (3)280
360 Substitute 3 for r and 80 for m
= 2 in 2 6.28 in 2 Simplify
Find the area of each sector. Give your answer in terms
of and rounded to the nearest hundredth.
3 in80
P
N
M
Finding the Area of the Sector
CONFIDENTIAL 29
B) sector EFG
A = r2m
360 Use formula for area of sector
= (6)2120
360 Substitute 6 for r and 120 for m
= 12 37.70 cm2 Simplify
G
F
E
6 cm120
CONFIDENTIAL 30
A circular plot with a 720 ft diameter is watered by a spray irrigation system. To the nearest square
foot, what is the area that is watered as the sprinkler rotates through an angle of 50 ?
A = r2m
360
= (360)250
360 d = 720 ft, r = 360 ft.
= 56.549 ft2 Simplify
CONFIDENTIAL 31
A segment of a circle is a region bounded by an arc and its chord. The shaded region in the
figure is a segment
CONFIDENTIAL 32
Area of a segment
area of sectorarea of segment area of triangle
=
=
-
-
CONFIDENTIAL 33
Finding the Area of a SegmentFind the area of segment ACB to the nearest hundredth.
12 in
60BC
A
Step 1 Find the area of sector ACB.
A = r2m
360 Use formula for area of a sector
= (12)260
360 Substitute 12 for r and 60 for m
= 24 in2
CONFIDENTIAL 34
BC
A
Step 2 Find the area of ACB. Draw altitute AD.
A = 1
2 bh =
1
2(12) (6 3) CD = 6 in and h = (6 3) in
= 36 3 in2 simplify
Step 3 area of segment = areaof sector ACB - area of ACB = 24 36 3 =13.04 in2
CONFIDENTIAL 35
Arc Length
TERM DIAGRAM LENGTH
Arc length is the distancealong an arc measured in linear
units. m
B
A
L = 2rm
360
CONFIDENTIAL 36
Finding Arc Length
Find each arc length. Give your answer in terms of and rounded to the nearest hundredth.
A) CD
L = 2rm
360 Use formula for arc length
= 2 (10)90
360 Substitute 10 for r and 90 for m
= 5 ft 15.71ft Simplify
90
10 ft
C
D
CONFIDENTIAL 37
You did a great job today!You did a great job today!