8.3 – area, volume and surface area area of plane regions rectangle 6 ft squaretriangle 2 ft 3 ft...
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8.3 – Area, Volume and Surface AreaArea of Plane Regions
Rectangle
6 ft
Square Triangle
2 ft
3 ft
3 ft 3 ft
4 ft
A = 6·2
A = 12 sq ft
A = l·w
A = 32
A = 9 sq ft
A = s·s = s2
A = ½ ·4·3
A = 6 sq ft
A = ½ l·w
A = ½ b·h
8.3 – Area, Volume and Surface AreaArea of Plane Regions
Triangle
4 m
Parallelogram Trapezoid
2 m
7 yd 12 cm
A = ½ ·4·2
A = 4 sq m
A = ½ b·h
A = 7·3
A = 21 sq yd
A = b·h
A = ½ ·20·9
A = 90 sq cm
A = ½ (b1 + b2)·h
3 yd 9 cm
8 cm
A = ½ (12 + 8)·9
8.3 – Area, Volume and Surface AreaCalculate the area of the plane region
24 – 18 =
A = A + A
A = 12 · 6 +6 m
24 m
18 m
12 m
18 m
6 m
6 m
18 – 12 = 6 m
18·18
A = 72 + 324
A = 396 sq m
8.3 – Area, Volume and Surface AreaArea of Plane Regions
Circle Exact Area Approximate Area
Diameter = 14 inches
A = 3.14 ·r2
sq in
A = ·r2
rd
rd
Calculate the area
r = 7 inches
Exact Area
A = ·r2
A = ·72
A = 49
Approximate Area
A = 3.14 ·r2
A = 3.14 ·72
A = 3.14 ·49
A = 153.86 sq in
Formulas for Volume and Surface Area
8.3 – Area, Volume and Surface Area
8.3 – Area, Volume and Surface AreaFormulas for Volume and Surface Area
Calculate the volume and surface area of a rectangular box (prism) that is 7 feet long, 3 feet wide and 4 feet high.
8.3 – Area, Volume and Surface Area
cu ft
V = l·w·h
V = 7·3·4
V = 21·4
V = 84
SA = 2lw + 2wh + 2hl
SA = 2(lw + wh + hl)
SA = 2(7·3 + 3·4 + 4·7)
SA = 2(21 + 12 + 28)
SA = 2(21 + 40)
SA = 2(61)
SA = 122 sq ft
Approximate the volume and surface area of a cylinder that has a radius of 5 inches and height of 9 inches. ( ≈ 3.14)
8.3 – Area, Volume and Surface Area
cu in
V = · r2 · h
V = 3.14·52·9
V = 706.5
SA = 2r2 + 2rh
SA = 3.14(50 + 90)
SA = 439.6 sq in
V = 3.14·25·9
V = 3.14·225
SA = 2·3.14·52 + 2·3.14·5·9
SA = 2·3.14·25 + 2·3.14·45
SA = 50·3.14 + 90·3.14
SA = 3.14(140)
Calculate the volume of a square-base pyramid that has a base side measurement of 3 meters and a height of 5.1 meters.
8.3 – Area, Volume and Surface Area
m3
V = (1/3)· b2 · h
V = (1/3)·32·5.1
V = 15.3
V = (1/3)·9·5.1
V = 3·5.1
Approximate the volume of a cone that has a radius of 4 yards and a height of 6 yards. Round the answer to the nearest tenth of a yard. Use 22/7 as the approximation of .
8.3 – Area, Volume and Surface Area
cu yd
V = (1/3) · r2 · h
V = (1/3)(22/7)·42·6
V = (1/3)(22/7)·16·6
V = (22/7)·16·2
V = (22/7)·32
V = 704/7
V = 100.6
8.4 – Linear Measurement
ftin 112
ydft 13
ydin 136
mift 15280
112
11
1
12
in
ftor
ft
in
13
11
1
3
ft
ydor
yd
ft
1280,5
11
1
280,5
ft
mior
mi
ft
U. S. Units of Length U. S. Unit Fractions
136
11
1
36
in
ydor
yd
in
8.4 – Linear Measurement
inx
ft6in
ft
12
1
126x
inx 72
Conversions
Convert 6 feet to inches.
ftx
yd8ft
yd
3
1
38x
ftx 24
Convert 8 yards to feet.
8.4 – Linear Measurement
ftx
in68ft
in
1
12
6812 x
12
68x
Conversions
Convert 68 inches to feet and inches.
ftx
yd5ft
yd
3
1
35x
15x
5 yd 2 ft =ftx 5 in8
Convert 5 yards 2 feet to feet.
15 + 2 =
17 ft
8.4 – Linear Measurement
ftx
in19ft
in
1
12
1912 x
12
19x
Conversions
Add 5 feet 8 inches to 8 feet 11 inches.
ftx 1 in7
5 feet 8 inches
8 feet 11 inches
13 feet 19 inches
13 feet 0 inches
1 feet 7 inches
14 feet 7 inches
8.4 – Linear Measurement
ftx
in28ft
in
1
12
2812 x
12
28x
Conversions
Multiply 4 feet 7 inches by 4.
ftx 2 in4
4 feet 7 inches
4
16 feet 28 inches
16 feet 0 inches
2 feet 4 inches
18 feet 4 inches
×
8.4 – Linear MeasurementConversions
A carpenter cuts 1 ft 9 in from a board of length 5 ft 8 in. What is the length of the remaining piece.
3 feet 11 inches
5 feet 8 inches
1 feet 9 inches
3 ft 11 in
–
5 feet 8 inches
1 feet 9 inches–
4 20
8.4 – Linear Measurement
kmm 11000
mcm 1100
cmmm 110
mmm 11000
11
10001
1000
1
km
mor
m
km
11
1001
100
1
m
cmor
cm
m
11
10001
1000
1
m
mmor
mm
m
Metric Units of Length Metric Unit Fractions
11
101
10
1
cm
mmor
mm
cm
8.4 – Linear Measurement
mmx
m5.2mm
m
1000
1
10005.2 x
500,2x
Conversions
Convert 2.5 m to millimeters.
kmx
m3500km
m
1
1000
35001000 x
1000
3500x
mm
Convert 3500 m to km.
5.3x km
8.4 – Linear Measurement
mmx
cm4.6mm
cm
10
1
104.6 x
64x
Conversions
Subtract 21 mm from 6.4 cm.
6421
43
43 mm
cmx
mm21
cm
mm
1
10
2110 x
10
21x
6.42.1
4.3
4.3 cm
1.2x
––
8.4 – Linear Measurement
mx
cm46.113m
cm
1
100
46.113100 x
100
46.113x
Conversions
Multiply 18.3 cm by 6.2 and convert the answer to meters.
1346.1x m
18.36.2
366
×
1098
11346
113.46 cm
8.4 – Linear Measurement
cmx
m8.0cm
m
100
1
1008.0 x80x
Conversions
A knitted scarf is currently 0.8 m long. If an additional 45 cm is knitted, how long will the scarf be?
8045
125
125 cm
mx
cm45m
cm
1
100
45100 x
100
45x
0.800.45
1.25
1.25 m
45.0x
+ +