11-3
Exercises
11-3 Exercises
KEYWORD: MG7 11-3
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
1. Vocabulary In a circle, the region bounded by a chord and an arc is called a
? . (sector or segment) seg.
−−−−
SEE EXAMPLE
1
p. 764
Find the area of each sector. Give your answer in terms of π and rounded to the
nearest hundredth.
2. sector PQR
3. sector JKL
9π m 2;
28.27 m 2
Èʓ
+
,
SEE EXAMPLE
2
p. 765
SEE EXAMPLE
3
p. 765
24π cm 2; nÊV“
75.40 cm 2
£ÎxÂ
_2 π ft ;
2
9
0.70 ft 2
™äÂ
ÓÊvÌ
ÓäÂ
If you finished Examples 1–4
Basic 12–34, 38–45
Average 12–35, 38–45
Advanced 12–45
Homework Quick Check
Multi-Step Find the area of each segment to the nearest hundredth.
6.
7.
Îʈ˜°
™äÂ
p. 766
*
If you finished Examples 1–2
Basic 12–15, 26
Average 12–15, 26, 35
Advanced 12–15, 26, 35, 37
4. sector ABC
5. Navigation The beam from a lighthouse is visible for a distance of 3 mi.
To the nearest square mile, what is the area covered by the beam as it sweeps in
an arc of 150°? 12 mi 2
SEE EXAMPLE 4
Assign Guided Practice exercises
as necessary.
8.
ÈäÂ
Óäʓ {xÂ
,
ÈÊV“
+
1.41 cm 2
36.23 m 2
2.57 in 2
Quickly check key concepts.
Exercises: 12, 15, 18, 20, 21, 24
*
Visual Point out the difference between arc measure
and arc length to students.
If an exercise asks for the measure
of an arc, the notation will be m AB .
Exercise 9 asks for EF , which is the
notation for arc length.
Find each arc length. Give your answer in terms of π and rounded to the nearest
hundredth.
{xÂ
9. EF
10. PQ
™Ê“
£ÈÊvÌ
*
4π ft; 12.57 ft
+
£ÓäÂ
6π m; 18.85 m
Reading Math Explain
that the word lunette In
Exercise 15 comes from
the Latin word luna, which means
“moon.” The lunette
ENGLISH
LANGUAGE
window looks like a
LEARNERS
crescent moon.
2 π in; 2.09 in.
11. an arc with measure 20° in a circle with radius 6 in. _
3
PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
12–14
15
16–18
19–21
1
2
3
4
Find the area of each sector. Give your answer in terms of π and rounded to the
nearest hundredth.
12. sector DEF
500
_
πm ;
2
3
523.60 m 2
13. sector GHJ
£xäÂ
Óäʓ _
45
π in 2;
2
70.69 in 2
14. sector RST
_
™Êˆ˜°
£ääÂ
47 π ft 2;
90
1.64 ft 2
,
{ÇÂ
-
ÓÊvÌ
/
Extra Practice
Skills Practice p. S24
Application Practice p. S38
15. Architecture A lunette is a semicircular
window that is sometimes placed above a
doorway or above a rectangular window.
To the nearest square inch, what is the
area of the lunette? 628 in 2
{äʈ˜°
11-3 Sector Area and Arc Length
ge07se_c11_0764_0769.indd 767
767
12/3/05 11:39:53 AM
KEYWORD: MG7 Resources
Lesson 11-3
767
Exercise 29 involves
using the formula
for arc length to
find the distance traveled by a bike
and to find the angle through which
the pedals must turn to move the
bike a certain distance. This exercise
prepares students for the Multi-Step
Test Prep on page 770.
Multi-Step Find the area of each segment to the nearest hundredth.
16.
17.
£äʓ
£ÊvÌ
xʈ˜°
28.54 m 2
ÈäÂ
/
-
0.09 ft 2
15.35 in 2
£ÓäÂ
Find each arc length. Give your answer in terms of π and rounded to the
nearest hundredth.
19. UV
Algebra As students work
through Exercise 29b,
encourage them to use
variables to solve for the angle
and then to substitute a distance of
4.5 ft in the formula.
{xÂ
,
18.
20. AB
6
xäÂ
£°xʓ
1
Math History
_
25
π mm;
18
4.36 mm
xʓ“
1 π ft; 0.31 ft
21. _
£ÈäÂ
_4 π m; 4.19 m
3
10
21. an arc with measure 9° in a circle with diameter 4 ft
22. Math History Greek mathematicians studied the
salinon, a figure bounded by four semicircles. What is the
perimeter of this salinon to the nearest tenth of an inch?
£Êˆ˜°
£Êˆ˜°
18.8 in.
Hypatia lived 1600
years ago. She is
considered one of
history’s most important
mathematicians.
She is credited with
contributions to
both geometry and
astronomy.
Tell whether each statement is sometimes, always, or never true.
23. The length of an arc of a circle is greater than the circumference of the circle. N
24. Two arcs with the same measure have the same arc length. S
25. In a circle, two arcs with the same length have the same measure. A
Find the radius of each circle.
26. area of sector
ABC = 9π 6
£ÓäÂ
27. arc length of
= 8π 12
EF
™äÂ
22
28. Estimation The fraction __
is an approximation for π.
7
. 11 in.
a. Use this value to estimate the arc length of XY
8
™äÂ
to
b. Use the π key on your calculator to find the length of XY
Çʈ˜°
8 decimal places. 10.99557429 in.
overestimate
c. Was your estimate in part a an overestimate or an underestimate?
9
29. This problem will prepare you for the Multi-Step
Test Prep on page 770.
The pedals of a penny-farthing bicycle are directly
connected to the front wheel.
a. Suppose a penny-farthing bicycle has a front
wheel with a diameter of 5 ft. To the nearest
tenth of a foot, how far does the bike move
3.9 ft when you turn the pedals through an angle of 90°?
b. Through what angle should you turn the pedals
in order to move forward by a distance of 4.5 ft?
Round to the nearest degree. 103°
11-3 PRACTICE A
11-3 PRACTICE C
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11-3 PRACTICE B
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Sector of a Circle
A sector of a circle is a region bounded by two
radii of the circle and their intercepted arc.
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11-3 RETEACH
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—
Reteach
LESSON
11-3 Sector Area and Arc Length
11-3 READING STRATEGIES
—
6
Chapter 11 Circles
M—
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9
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The area of a sector of a circle is given by the
2 m°
.
formula A ⫽ ␲r ____
360°
sector ABC
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12/3/05 11:40:00 AM
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120°
QCM
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area of
segment ABC
⫽
area of sector
ABC
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!
segment ABC
area of 䉭ABC
IN
Find the area of each sector. Give your answer in terms of ␲ and
rounded to the nearest hundredth.
8
4
8 ft
:
1. sector CDE
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90°
3
27␲ in ; 84.82 in
Find the area of each segment to the nearest hundredth.
—
2
2
7␲ cm ; 21.99 cm
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1.14 in
2
5.80 m
2
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