Section 9.4
Volume and
Surface Area
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
INB Table of Contents
Date
2.3-2
Topic
Page #
June 10, 2013
Volume and Surface Area Formulas
22
June 10, 2013
Section 9.4 Notes
23
June 10, 2013
Test #2 Practice Workspace
24
June 10, 2013
Test #2 Practice Test
25
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Volume
Surface Area
9.4-3
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
Volume is the measure of the capacity of
a three-dimensional figure.
It is the amount of material you can put
inside a three-dimensional figure.
Surface area is sum of the areas of the
surfaces of a three-dimensional figure.
It refers to the total area that is on the
outside surface of the figure.
9.4-4
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Volume
Solid geometry
is the study of three-dimensional solid
figures, also called space figures.
Volumes is measured in cubic units such
as cubic feet or cubic meters.
Surface area is measured in square units
such as square feet or square meters.
9.4-5
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
9.4-6
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Determine the volume and surface
area of the following threedimensional
figure.
Solution
3
V  lwh  11  3  6  198 ft
SA  2lw  2wh  2lh
 2 11  3  2  3  6  2 11  6
2
 66  36  132  234 ft
9.4-7
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Determine the volume and surface
area of the following threedimensional
figure. When appropriate,
use the π key on your
calculator and round
your answer to the
nearest hundredths.
9.4-8
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Solution
V  r h    4 8
 128
3
 402.12 m
2
2
SA  2 rh  2 r
2
 2  4  8  2  4
2
 64  32  96  301.59 m
2
9.4-9
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Determine the volume and surface
area of the following threedimensional
figure. When appropriate,
use the π key on your
calculator and round
your answer to the
nearest hundredths.
9.4-10
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Solution
1 2
1
2
V  r h   3 8
3
3
 24
3
 75.40 m
SA   r   r r  h
2
2
2
  3   3 3  8
2
2
2
 9  3 73  108.80 m
2
9.4-11
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Determine the volume and surface
area of the following three-dimensional
figure. When appropriate,
use the π key on your
calculator and round
your answer to the
nearest hundredths.
9.4-12
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 1: Volume and Surface Area
Solution
4 3 4
3
V  r   9
3
3
 972
3
 3053.63 cm
SA  4 r
2
 4    9  4    81
2
 324  1017.88 cm
2
9.4-13
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Polyhedra
A polyhedron is a closed surface formed
by the union of polygonal regions.
9.4-14
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Euler’s Polyhedron Formula
number
number
Number
of
of
of
= 2
+
–
faces
edges
vertices
9.4-15
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Prism
The prisms illustrated are all right
prisms.
When we use the word prism in this
book, we are referring to a right prism.
9.4-16
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Volume of a Prism
V = Bh,
where B is the area of the base and h
is the height.
9.4-17
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Example 6: Volume of a
Hexagonal Prism Fish Tank
Frank Nicolzaao’s fish
tank is in the shape of a
hexagonal prism. Use
the dimensions shown in
the figure and the fact
that 1 gal = 231 in3 to
a) determine the
volume of the fish tank
in cubic inches.
9.4-18
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Example 6: Volume of a
Hexagonal Prism Fish Tank
Solution
Area of hexagonal base:
two identical trapezoids
1
Atrap  h b1  b2
2
1
2
Atrap  (8)(16  8)  96 in
2
Areabase = 2(96) = 192 in2

9.4-19

Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Volume of a
Hexagonal Prism Fish Tank
Solution
Volume of fish tank:
V  Bh
 192  24
3
 4608 in
9.4-20
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 6: Volume of a
Hexagonal Prism Fish Tank
b) determine the volume
of the fish tank in
gallons (round your
answer to the nearest
gallon).
Solution
4608
 19.95 gal
V 
231
9.4-21
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Pyramid
A pyramid is a polyhedron with one
base, all of whose faces intersect at a
common vertex.
9.4-22
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Volume of a Pyramid
1
V  Bh
3
where B is the area of the base and h
is the height.
9.4-23
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Example 8: Volume of a Pyramid
Determine the volume of the pyramid.
Solution
Area of base = s2 = 22
= 4 m2
1
1
V  Bh   4  3
3
3
3
4m
The volume is 4 m3.
9.4-24
Copyright 2013, 2010, 2007, Pearson, Education, Inc.