Transcript Chapter 8 - Sections 3-4

8.3 – Area, Volume and Surface Area
Area of Plane Regions
Rectangle
Square
3 ft
2 ft
6 ft
Triangle
3 ft
A = l·w
A = 6·2
A = s·s = s2
A = 32
A = 12 sq ft
A = 9 sq ft
3 ft
4 ft
A = ½ l·w
A = ½ b·h
A = ½ ·4·3
A = 6 sq ft
8.3 – Area, Volume and Surface Area
Area of Plane Regions
Triangle
Parallelogram
Trapezoid
8 cm
2m
4m
3 yd
7 yd
A = ½ b·h
A = ½ ·4·2
A = b·h
A = 7·3
A = 4 sq m
A = 21 sq yd
9 cm
12 cm
A = ½ (b1 + b2)·h
A = ½ (12 + 8)·9
A = ½ ·20·9
A = 90 sq cm
8.3 – Area, Volume and Surface Area
Calculate the area of the plane region
24 m
A = A + A 
12 m


6m
18 m
A = 12 · 6 + 18·18
A = 72 + 324
6m
A = 396 sq m
18 m
24 – 18 = 6 m
18 – 12 = 6 m
8.3 – Area, Volume and Surface Area
Area of Plane Regions
Circle
Exact Area
A = ·r2
Approximate Area
A = 3.14 ·r2
r
d
Calculate the area
Exact Area
r
d
Diameter = 14 inches
r = 7 inches
A = ·r2
A = ·72
A = 49 sq in
Approximate Area
A = 3.14 ·r2
A = 3.14 ·72
A = 3.14 ·49
A = 153.86 sq in
8.3 – Area, Volume and Surface Area
Formulas for Volume and Surface Area
8.3 – Area, Volume and Surface Area
Formulas for Volume and Surface Area
8.3 – Area, 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.
V = l·w·h
SA = 2lw + 2wh + 2hl
V = 7·3·4
SA = 2(lw + wh + hl)
V = 21·4
V = 84 cu ft
SA = 2(7·3 + 3·4 + 4·7)
SA = 2(21 + 12 + 28)
SA = 2(21 + 40)
SA = 2(61)
SA = 122 sq ft
8.3 – Area, Volume and Surface Area
Approximate the volume and surface area of a cylinder that
has a radius of 5 inches and height of 9 inches. ( ≈ 3.14)
V =  · r2 · h
SA = 2r2 + 2rh
V = 3.14·52·9
SA = 2·3.14·52 + 2·3.14·5·9
V = 3.14·25·9
SA = 2·3.14·25 + 2·3.14·45
V = 3.14·225
SA = 50·3.14 + 90·3.14
V = 706.5 cu in
SA = 3.14(50 + 90)
SA = 3.14(140)
SA = 439.6 sq in
8.3 – Area, Volume and Surface Area
Calculate the volume of a square-base pyramid that has a base
side measurement of 3 meters and a height of 5.1 meters.
V = (1/3)· b2 · h
V = (1/3)·32·5.1
V = (1/3)·9·5.1
V = 3·5.1
V = 15.3 m3
8.3 – Area, Volume and Surface Area
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 .
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 cu yd
8.4 – Linear Measurement
U. S. Units of Length
U. S. Unit Fractions
12 in  1 ft
12 in
3 ft  1 yd
1 ft
12 in
36 in  1 yd
3 ft
1 yd
5280 ft  1 mi
1
1
or
or
1 ft
1 yd
3 ft
36 in
1 yd
1
or
1 yd
5 , 280 ft
1 mi
1
1
1
36 in
1
or
1 mi
5 , 280 ft
1
8.4 – Linear Measurement
Conversions
Convert 6 feet to inches.
6 ft
x in

Convert 8 yards to feet.
1 ft
8 yd
12 in
x ft

1 yd
3 ft
x  6  12
x  83
x  72 in
x  24 ft
8.4 – Linear Measurement
Conversions
Convert 68 inches to feet
Convert 5 yards 2 feet to
and inches.
feet.
68 in
x ft

12 in
5 yd
1 ft
x ft
12 x  68
68
x
12
x  5 ft 8 in

1 yd
3 ft
x  53
x  15
5 yd 2 ft = 15 + 2 =
17 ft
8.4 – Linear Measurement
Conversions
Add 5 feet 8 inches to 8 feet 11 inches.
5 feet 8 inches
8 feet 11 inches
13 feet 0 inches
1 feet 7 inches
13 feet 19 inches
14 feet 7 inches
19 in
x ft

12 in
1 ft
12 x  19
19
x
12
x  1 ft 7 in
8.4 – Linear Measurement
Conversions
Multiply 4 feet 7 inches by 4.
4 feet 7 inches
× 4
16 feet 0 inches
2 feet 4 inches
16 feet 28 inches
18 feet 4 inches
28 in
x ft

12 in
1 ft
12 x  28
28
x
12
x  2 ft 4 in
8.4 – Linear Measurement
Conversions
A carpenter cuts 1 ft 9 in from a board of length 5 ft 8 in.
What is the length of the remaining piece.
5 feet 8 inches
– 1 feet 9 inches
4
20
5 feet 8 inches
– 1 feet 9 inches
3 feet 11 inches
3 ft 11 in
8.4 – Linear Measurement
Metric Units of Length
Metric Unit Fractions
1000 m  1 km
1 km
100 cm  1 m
1000 m
1 km
10 mm  1 cm
1m
100 cm
1000 mm  1 m
1
1
or
or
100 cm
1 cm
1000 mm
1
1
1m
1
or
10 mm
1m
1000 m
10 mm
1
1 cm
1
or
1000 mm
1m
1
8.4 – Linear Measurement
Conversions
Convert 2.5 m to millimeters.
Convert 3500 m to km.
2 .5 m
x mm

1m
3500 m
1000 mm
x km
x  2 . 5  1000
x  2 , 500 mm

1000 m
1 km
1000 x  3500
x
3500
1000
x  3 . 5 km
8.4 – Linear Measurement
Conversions
Subtract 21 mm from 6.4 cm.
6 . 4 cm

x mm
1 cm
21 mm
10 mm
x cm
x  6 . 4  10
x  64

10 mm
1 cm
10 x  21
x
21
10
64
– 21
43
43 mm
6.4
– 2.1
4.3
4.3 cm
x  2 .1
8.4 – Linear Measurement
Conversions
Multiply 18.3 cm by 6.2 and convert the answer to meters.
18.3
× 6.2
366
1098
11346
113.46 cm
113 . 46 cm

100 cm
xm
1m
100 x  113 . 46
x
113 . 46
100
x  1 . 1346 m
8.4 – Linear Measurement
Conversions
A knitted scarf is currently 0.8 m long. If an additional 45 cm
is knitted, how long will the scarf be?
0 .8 m

x cm
1m
45 cm
100 cm
xm
x  0 . 8  100
x  80
80
+ 45
125
125 cm

100 cm
1m
100 x  45
x
45
100
0.80
+ 0.45
1.25
1.25 m
x  0 . 45