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·wA = 32
A = 9 sq ft
A = s·s = s2
A = ½ ·4·3
A = 6 sq ft
A = ½ l·wA = 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·hA = 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 AreaA = ·r2
A = ·72
A = 49
Approximate AreaA = 3.14 ·r2
A = 3.14 ·72
A = 3.14 ·49A = 153.86 sq in
Formulas for Volume and Surface Area8.3 – 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·hV = 7·3·4V = 21·4V = 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 · hV = 3.14·52·9
V = 706.5
SA = 2r2 + 2rh
SA = 3.14(50 + 90)
SA = 439.6 sq in
V = 3.14·25·9V = 3.14·225
SA = 2·3.14·52 + 2·3.14·5·9SA = 2·3.14·25 + 2·3.14·45SA = 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 · hV = (1/3)·32·5.1
V = 15.3
V = (1/3)·9·5.1V = 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 · hV = (1/3)(22/7)·42·6V = (1/3)(22/7)·16·6V = (22/7)·16·2V = (22/7)·32V = 704/7V = 100.6
8.4 – Linear Measurement
ftin 112
ydft 13
ydin 136
mift 15280
11211
112
inftor
ftin
1311
13
ftydor
ydft
1280,511
1280,5
ft
miormift
U. S. Units of Length U. S. Unit Fractions
1361
1136
inyd
orydin
8.4 – Linear Measurement
inxft6
inft
121
126x
inx 72
ConversionsConvert 6 feet to inches.
ftxyd8
ftyd
31
38x
ftx 24
Convert 8 yards to feet.
8.4 – Linear Measurement
ftxin68
ftin
112
6812 x
1268
x
ConversionsConvert 68 inches to feet and inches.
ftxyd5
ftyd
31
35x
15x
5 yd 2 ft =ftx 5 in8
Convert 5 yards 2 feet to feet.
15 + 2 =
17 ft
8.4 – Linear Measurement
ftxin19
ftin
112
1912 x
1219
x
ConversionsAdd 5 feet 8 inches to 8 feet 11 inches.
ftx 1 in7
5 feet 8 inches8 feet 11 inches
13 feet 19 inches
13 feet 0 inches1 feet 7 inches
14 feet 7 inches
8.4 – Linear Measurement
ftxin28
ftin
112
2812 x
1228
x
ConversionsMultiply 4 feet 7 inches by 4.
ftx 2 in4
4 feet 7 inches4
16 feet 28 inches
16 feet 0 inches2 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 inches1 feet 9 inches
3 ft 11 in
–
5 feet 8 inches1 feet 9 inches–
4 20
8.4 – Linear Measurement
kmm 11000
mcm 1100
cmmm 110
mmm 11000
11
10001
10001
kmm
orm
km
11
1001
1001
mcm
orcmm
11
10001
10001
mmm
ormmm
Metric Units of Length Metric Unit Fractions
11
101
101
cmmm
ormmcm
8.4 – Linear Measurement
mmxm5.2
mmm
10001
10005.2 x
500,2x
ConversionsConvert 2.5 m to millimeters.
kmxm3500
kmm
11000
35001000 x
10003500
xmm
Convert 3500 m to km.
5.3x km
8.4 – Linear Measurement
mmxcm4.6
mmcm
101
104.6 x
64x
ConversionsSubtract 21 mm from 6.4 cm.
64214343 mm
cmxmm21
cmmm
110
2110 x
1021
x
6.42.14.34.3 cm
1.2x
– –
8.4 – Linear Measurement
mxcm46.113
mcm
1100
46.113100 x
10046.113
x
ConversionsMultiply 18.3 cm by 6.2 and convert the answer to meters.
1346.1x m
18.36.2
366×
109811346113.46 cm
8.4 – Linear Measurement
cmxm8.0
cmm
1001
1008.0 x80x
ConversionsA knitted scarf is currently 0.8 m long. If an additional 45 cm is knitted, how long will the scarf be?
8045
125125 cm
mxcm45
mcm
1100
45100 x
10045
x
0.800.451.251.25 m
45.0x
+ +
