6.8areas of circles and sectors theorem 6.20: area of a circle the area of a circle is times the...
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6.8 Areas of Circles and Sectors
Theorem 6.20: Area of a CircleThe area of a circle is times the square of the radius.
_____ Ar
2 r
6.8 Areas of Circles and Sectors
Example 1 Use the formula for area of a circleUse the formula for area of a circle
Find the indicated measure.a. Area
Solution
m 2.4
Write formula for area of a circle.2 a. rA
Substitute ____ for r.2.4 2___ 2.4
Simplify. _____ 64.17Use a calculator. m _____ 2 42.55
6.8 Areas of Circles and Sectors
Example 1 Use the formula for area of a circleUse the formula for area of a circle
Find the indicated measure.a. Area b. Diameter
Solution
m 2.42in 201A
Write formula for area of a circle.2 b. rA
Substitute _____ for A.2012 ___ r201Divide each side by ___. _____ 2r98.63Find the positive sq. rt. of each side.r___8
The radius is about ___ inches, so the diameter is about ___ inches8 16
6.8 Areas of Circles and Sectors
Theorem 6.21: Area of a SectorThe ratio of the area of a sector of a circle to the area of the whole circle r2) is equal to the ratio of the measure of the intercepted arc to 360o.
P
A
B
ror ,360
APBsector of Area
2 rABm
____360
APBsector of Area
ABm 2 r
6.8 Areas of Circles and Sectors
Example 2 Find areas of sectorsFind areas of sectors
Find the area of the sector formed by
SolutionStep 1 Find the measure of the minor and major arcs.
RQS. Q
R
S
P o635
and ____ ____, Because mRSRQSm 63 63________360 mRPS 63 297
6.8 Areas of Circles and Sectors
Example 2 Find areas of sectorsFind areas of sectors
Find the area of the sector formed by
Solution
RQS. Q
R
S
P o635
Step 2 Find the areas of the small and large sectors.
2 360
rmRS
Area of small sector =
2__ 360
63 5
_____ 74.13
6.8 Areas of Circles and Sectors
Example 2 Find areas of sectorsFind areas of sectors
Find the area of the sector formed by
Solution
RQS. Q
R
S
P o635
Step 2 Find the areas of the small and large sectors.
2 360
rmRPS
Area of large sector =
2__ 360
297 5
_____ 80.64The areas of the small and large sectors are about _______ square units and _______ square units, respectively.
74.1380.64
6.8 Areas of Circles and Sectors
Example 3 Use the Area of a Sector TheoremUse the Area of a Sector Theorem
Use the diagram to find the area of
Solution
C
A
B
452m 22A .C.
of Area360
mABArea of sector ACB = .C.
of Area360
____
4522 C.
of Area____ .C.176
The area of is ______ square meters.C. 176
6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.
1. Find the radius of the circle.
2ft 154A 2 rA 2 154 r
2r 02.49r 7 ft
6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.
2. Find the areas of the sectors formed by RQS. P
R
S
Q 106
ft 92
360r
mRS
Area of small sector =
2 360
106
9 93.74 2ft
2 360
rmRPS
Area of large sector =
2 360
254
9 54.179 2ft
6.8 Areas of Circles and SectorsCheckpoint. Complete the following exercise. Checkpoint. Complete the following exercise.
3. Find the area of G..
F
H
G2yd 6.4A 08
of Area360
mFHArea of sector FGH = G.
of Area360
80
4.6 G.
of Area G.8.28
8.28 2yd
6.7 Circumference and Arc Length
Pg. 242, 6.8 #1-22