Transcript Chapter 8

Chapter 8
8-1 Estimating Perimeter and Area
 Perimeter – total distance around the figure
 Area – number of square units a figure encloses
8-1 Estimating Perimeter and Area-answers
 Perimeter – total distance around the figure
 Area – number of square units a figure encloses
12ft ; truck cab quite tall
8 in; book is not very wide
8 in; pizza not very big
2ft ; bathtub is not very deep
8-1 Estimating Perimeter and Area
8-1 Estimating Perimeter and Area-answers
10 yd
16 yd
12 yd
13 yd
8-1 Estimating Perimeter and Area
8-1 Estimating Perimeter and Area-answers
about 7 cm2
ft
about 19 cm2
about 10 cm2
in
about 18 cm2
mi2
8-2 Area of a Parallelogram
 height of a parallelogram – length of a
perpendicular segment connecting base of
parallelogram to the other.
 Area of parallelogram:
Area = bh
8-2 Area of a Parallelogram
8-2 Area of a Parallelogram-answers
25 m2
60 m2
392 m2
12 ft2
150 in2
8-2 Area of a Parallelogram
8-2 Area of a Parallelogram-answers
3ft by 7 ft
8-3 Perimeter and Area of a Triangle
 base of a triangle – any side can be considered base
 height of triangle – length of perpendicular segment
from a vertex to the bases opposite or and extension of
base
Area of triangle = ½ bh or bh/2
8-3 Perimeter and Area of a Triangle
8-3 Perimeter and Area of a Triangle - answers
8.2 ft
23.9 in
34.6 in
416 ft
8-3 Perimeter and Area of a Triangle
8-3 Perimeter and Area of a Triangle-ans
299 cm2
59.22 mi2
26.8 km2
1325 yd2
4, 4, 4; 5, 5, 2
8-4 Area of Other Figures
 bases of trapezoid – two parallel sides of a
trapezoid; b1 and b2
 height of trapezoid – length of perpendicular
segment connecting bases
Area of trapezoid = ½h(b1 + b2) or h(b1 + b2)
2
8-4 Area of Other Figures
8-4 Area of Other Figures-answers
33 ft2
98 m2
748
ft2
838 km2
33.25 in2
2586 yd2
8-5 Circumference and Area of a Circle
Circumference – is the distance around the
outside of a circle
Π – the ratio of a circle’s circumference to its
diameter d. Π is nonterminating and nonrepeating
Π is approximate 3.14 or 22/7
8-5 Circumference and Area of a Circle
8-5 Circumference and Area of a Circle-answers
C = Πd
= Π*50
= 157.1 cm
C = 2Πr
= 2*Π*40
= 251.3 in
8-5 Circumference and Area of a Circle
8-5 Circumference and Area of a Circle-answers
C = Πd
= Π*17
= 53.4 mm
C = 2Πr
= 2*Π*7
= 44.0 cm
8-5 Circumference and Area of a Circle
8-5 Circumference and Area of a Circle
A = Πr2
= Π*62
= 36 Π
= 113 in2
A = Πr2
= Π*152
= 225 Π
= 707 ft2
8-5 Circumference and Area of a Circle
A = Πr2
= Π*112
= 121 Π
= 380 cm2
A = Πr2
= Π*252
= 625 Π
= 1963 cm2
8-8 Three-Dimensional Figures
 3-D figure – figure that does not lie in plane
 face – flat surface of solid shaped like polygon
 edge – segment formed by intersection of 2 faces
 prism – 3-D figure with two parallel and
congruent polygonal faces, called bases
8-8 Three-Dimensional Figures
Prisms are named for the
shape of its bases. Name
this prism.
8-8 Three-Dimensional Figures
Cube - rectangular
prism with faces that
are all squares
Cylinder - bases are
circles
8-8 Three-Dimensional Figures
Pyramids – are made up of
triangular faces that meet at
one point, called a vertex
Cone – one base
that is a circle and
one vertex
8-8 Three-Dimensional Figures
Sphere – set of all points in
space that are same
distance from a center point
8-8 Three-Dimensional Figures
Sphere – set of all points in
space that are same
distance from a center point
Rectangle,
rectangular prism
triangle,
Triangular prism
pentagon,
Pentagonal prism
8-8 Three-Dimensional Figures
8-8 Three-Dimensional Figures
sphere
cylinder
cone
Rectangular
pyramid
Hexagonal
pyramid
cone
8-9 Surface Area of Rectangular Prisms
Net – two – dimensional pattern that you can fold
into a 3-d figure
8-9 Surface Area of Rectangular Prisms
Net – two – dimensional pattern that you can fold
into a 3-d figure
Draw a net for the triangular
prism.
1) First label the bases and
the side.
2) Then draw the net.
8-9 Surface Area of Rectangular Prisms-answers
Net – two – dimensional pattern that you can fold
into a 3-d figure
8-9 Surface Area of Rectangular Prisms
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Rectangular Prisms-answers
Surface Area – sum of all the area of the faces of
a prism
SA = (5+4+5+4)6 + (2*5*4)
= 108 + 40
= 148 in2
TOP = 5*4 =
Bottom = 5 * 4 =
Left
=6*5=
Right
=6*5=
Front
= 6 *4 =
Back
=6*4=
20
20
30
30
24
+24
148 in2
8-9 Surface Area of Rectangular Prisms
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Rectangular Prisms
Surface Area – sum of all the area of the faces of
a prism
SA = Ph + 2B
= (7+4+7+4)6 + (2*7*4)
= 132 + 56
= 188 m2
TOP = 7*4 =
Bottom = 7 * 4 =
Left
=6*4=
Right
=6*4=
Front
= 6 *7 =
Back
=6*7=
28
28
24
24
42
+42
188 m2
8-9 Surface Area of Rectangular Prisms
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Rectangular Prisms-ans
Surface Area – sum of all the area of the faces of
a prism
SA = Ph + 2B
= (1+1+1+1)2 + (2*1*1)
=8+2
= 10 ft2
TOP = 1*1 =
Bottom = 1* 1 =
Left
=1*2=
Right
=1*2=
Front
= 1 *2 =
Back
=1*2=
1
1
2
2
2
+2
10 ft2
8-9 Surface Area of Triangular Prisms
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Triangular Prisms-ans
Surface Area – sum of all the area of the faces of
a prism
SA = Ph + 2B
= (9+12+15)4 + 2((9*12)/2)
= 144 + 108
= 252 cm2
TOP (triangle) = 9 * 12 / 2 = 54
Bottom (triangle)= 9 * 12 / 2 = 54
Left (rectangle) = 9*4
= 36
Front (rectangle) = 15*4
= 60
Back (rectangle) = 12 * 4
= +48
252 cm2
8-9 Surface Area of Triangular Prisms
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Triangular Prisms-ans
Surface Area – sum of all the area of the faces of
a prism
SA = Ph + 2B
=(6+8+10)9 + 2((6*8)/2)
= 216 + 48
= 264 m2
Left (triangle) = 6 * 8 / 2 = 24
Right (triangle)= 6 * 8 / 2 = 24
Front (rectangle) = 9*10 = 90
Back (rectangle) = 9*6
= 54
Bottom (rectangle) = 8*9 = +72
264 m2
8-9 Surface Area of Cylinders
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Cylinders
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Cylinders-ans
Surface Area – sum of all the area of the faces of
a prism
SA = 2Πrh + 2Πr2
= 2Π10*15 + 2Π102
= 942 + 628
= 1570 yd2
8-9 Surface Area of Cylinders
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Cylinders-ans
Surface Area – sum of all the area of the faces of
a prism
SA = 2Πrh + 2Πr2
= 2Π5*20 + 2Π52
= 628 + 157
= 785 cm2
8-9 Surface Area of Cylinders
Surface Area – sum of all the area of the faces of
a prism
8-9 Surface Area of Cylinders-ans
Surface Area – sum of all the area of the faces of
a prism
SA = 2Πrh + 2Πr2
= 2Π10*45 + 2Π102
= 2826 + 628
= 3454 m2
8-10 Volume of Prisms and Cylinders
Volume – number of cubic units needed to fill
the space INSIDE the figure
Cubic unit – a cube with edges one unit long
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders
Volume of a Rectangular Prism
V = Bh
= area of base * height
=l*w*h
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders-answers
V = Bh
=l*w*h
= 20 * 7 * 8
= 1120 in3
V = Bh
=l*w*h
= 8 * 10 * 8
= 640 ft3
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders-ans
V = Bh
= b*h * h
2
= 6*6* 8
2
= 192 cm3
V = Bh
= b*h * h
2
= 3*4* 5
2
= 30 in3
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders-ans
V = Bh
= b*h * h
2
= 12*28* 10
2
= 1680 m3
8-10 Volume of Prisms and Cylinders
Find the height of each rectangular prism given the
volume, length, and width.
V = 3375 m3
V = 900 ft3
L = 15 m
W = 15 m
H= ?
L= 45 ft
W = 2 ft
H=?
8-10 Volume of Prisms and Cylinders-ans
Find the height of each rectangular prism given the
volume, length, and width.
V = 3375 m3
V = 900 ft3
L = 15 m
W = 15 m
H = ? 15 m
L= 45 ft
W = 2 ft
H = ? 10 ft
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders-ans
V = Bh
= Πr2* h
= Π 12 * 10
= 31 ft3
V = Bh
= Πr2* h
= Π 142 * 80
= 49260 m3
8-10 Volume of Prisms and Cylinders
8-10 Volume of Prisms and Cylinders-ans
V = Bh
= Πr2* h
= Π 62 * 18
= 2036 in3