Chapter 7 Lessons 7

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Transcript Chapter 7 Lessons 7

Area
Area of
Circle
Area of
Sector
Area of
Segment
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
50
50
50
Segment
Area
Probability Probability
Find the area of the circle. Leave your answer in
terms of
.
A  r
3.6 m
2
A   (3.6)
2
A  12.96
Find the area of the circle. Leave your answer in
terms of
.
A  r
4.1 m
2
A   (2.05)
A  4.2
2
Find the area of the circle. Use π = 3.14.
A  r
2
A   (1.15)
A  4.15
2
Find the area of the circle. Use π = 3.14.
A  r
2
A   (1.9)
A  11.3
2
The figure represents the overhead view of a
deck surrounding a hot tub. What is the area of
the deck? Round to the nearest tenth.
L arg e
Sm all
A  r
A  r
2
2
A   (2.7) A   (4.9)
A  7.3
A  24.01
2
L arg e  Sm all
24.01  7.3
75.4  22.9
52.5
2
Find the area of the figure to the nearest tenth.
measure of arc
360°
105°
9
 r
105
2
  (9)
360
.29   81
.29  254.5
73.8
2
Find the area of a sector with a central angle of
180° and a diameter of 5.6 cm. Round to the
nearest tenth.
measure of arc
360°
 r
180
2
  ( 2.8)
360
.5   7.84
.5  24.6
12.3
2
Find the area of sector ZOM. Leave your answer
in terms of π.
measure of arc
360°
 r
72
2
  (20)
360
.2   400
80
2
Find the area of sector ACB. Leave your answer in terms of π.
mACB
 r 2
360
100
  (6)2
360
10
50
Find the area of the shaded portion of the
figure. Dimensions are in feet. Round your
answer to the nearest tenth.
Trapezoid
Circle
1
A  h (b1  b2 )
2
1
A  (8)(8  9)
2
A  4(17)
A  r
A  68
2
A   ( 4)
A  16
Shaded
A  68  16
A  68  50.24
A  17.8
2
Find the area of the triangle. Leave your answer
in simplest radical form.
Find height.
18 cm
10 cm
a 2  b2  c 2
10 cm
Not drawn to scale
1
A  bh
2
1
A  (18)( 19 )
2
A  9 19
92  b 2  102
81  b 2  100
b 2  19
b  19
Find the area of the shaded segment. Round your
answer to the nearest tenth.
Find the area of sector AOB.
Find the area of the segment.
Find the area of ∆ AOB.
The area of the segment is
about 28.5 in.2
Find the exact area of the shaded region.
1.) Find the area of the sector.
2
measure of arc
360°
120
  (24)2
360
.33   576
 r
.33  1809.6
597.2
2.) Find the area of the triangle.
LL=√3•SL
30°
60° 24
hyp.=2•SL
24=2•SL
12=SL
LL=12√3
1
bh
2
1
A  (12)(24 3 )
2
A  144 3
A
3.) Subtract
597.2 - 144√3
597.2 - 249.4
348
A circle has a radius of 24 ft. Find the are of the smaller
segment of the circle determined by a 120° arc. Round
your answer to the nearest tenth.
Find the area of the sector.
120
  (24 )2
360
1
 576
3
192
Find the area of ∆ AOB.
1
(24 3 )(12)
2
249 .4
24
60°
120°
24
hyp.= 2•SL
LL=√3•SL
24=2•SL
LL=√3•12
12=SL
LL=12√3
192  249 .4
Find the area
353of
.48the segment.
The area of the segment is
about 353.5 ft.2
Find the probability that a point chosen at random
from
is on the segment
A B C D E F G H I J K
0
1
2
3
4
5 6
favorable
possible
CJ
AK
92
10
7
10
7
8
9
Lenny’s favorite radio station has this schedule:
news 13 min, commercials 2 min, music 45 min. If
Lenny chooses a time of day at random to turn on
the radio to his favorite station, what is the
probability that the news will be on?
favorable
possible
news
total
13
60
What is the probability that a point chosen at
random on the grid will lie in the unshaded region?
favorable
possible
unshaded
total
40
64
5
8
A fly lands at a random point on the ruler's edge. Find the
probability that the point is between 3 and 7.
40
P(landing between 3 and 7) =
7-3=4
=
=
Anna's bus runs every 25 minutes. If she arrives at her bus
stop at a random time, what is the probability that she will have
to wait at least 10 minutes for the bus?
Assume that a stop takes very little time, and let
represent
the 25 minutes between buses.
If Anna arrives at any time between A and C, she has to wait at
least 10 minutes until B.
P(waiting at least 10 min) =
=
, or
The probability that Elena will have to wait at least 10 minutes
for the bus is
or 60%.
If a dart hits the target at random, what it the
probability that it will land in the shaded region?
favorable
possible
 (2)
2
 (6)
4
36
2
1
9
The radius of the bull’s-eye of the dartboard is 8
inches. The radius of each concentric circle is 8
inches more than the radius of the circle inside it.
If a dart lands at random on the dartboard, what
is the probability that the dart will hit in area C?
favorable
possible
 (24)2   (16)2
 (32)2
576  256
1024
320
1024
5
16
Assume that a dart you throw will land on the 1-ft square
dartboard and is equally likely to land at any point on the board.
Find the probability of hitting each of the blue, yellow, and red
30
regions. The radii of the concentric
circles are 1, 2, and 3
inches, respectively.
The probabilities of hitting the blue, yellow, and red regions
are about 2.2%, 6.5%, and 10.9%, respectively.
40
50