Transcript Space Figures, Volume, and Surface Area

Chapter 9
Geometry
© 2008 Pearson Addison-Wesley.
All rights reserved
Chapter 9: Geometry
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Points, Lines, Planes, and Angles
Curves, Polygons, and Circles
Perimeter, Area, and Circumference
The Geometry of Triangles: Congruence,
Similarity, and the Pythagorean Theorem
Space Figures, Volume, and Surface Area
Transformational Geometry
Non-Euclidean Geometry, Topology, and Networks
Chaos and Fractal Geometry
9-5-2
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Chapter 1
Section 9-5
Space Figures, Volume, and Surface
Area
9-5-3
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Space Figures, Volume, and Surface
Area
• Space Figures
• Volume and Surface Area of Space Figures
9-5-4
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Space Figures
Space figures take three dimensions of
space to represent the figure.
One important group of space figures is a group
called polyhedra. The faces of these figures are
made only of polygons.
9-5-5
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Regular Polyhedra (Platonic Solids)
Name
Description
Tetrahedron
4 equilateral triangles
Hexahedron
6 squares (cube)
Octahedron
Groups of 4 regular triangles
Dodecahedron
Groups of 3 regular pentagons
Icosahedron
Groups of 5 regular triangles
See pictures on the next slide.
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Space Figures
9-5-7
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Space Figures
The next slide shows space includes two other
polyhedra: pyramids and prisms. Pyramids are
made of triangular sides and a polygonal base.
Prisms have two faces in parallel planes; these faces
are congruent polygons.
The next slide also shows a torus which is a
doughnut-shaped solid and figures made up in part of
circles including right circular cones and right
circular cylinders.
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Space Figures
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Volume and Surface Area
Volume is a measure of capacity of a space
figure. Volume is measured in cubic units.
Surface Area is the total area that would be
covered if the space figure were “peeled”
and the peel laid flat. Surface area is
measured in square units.
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Volume of Surface Area of a Box
The volume V and surface area S of a box
with length l, width w, and height h is
given by the formulas
V  lwh and S  2lw  2lh  2hw.
h
l
w
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Example: Volume of Surface Area of a
Box
Find the volume and surface area of the
box below.
3 in.
7 in.
Solution
2 in.
V  7(2)(3)  42 in.
3
S  2(7)(2)  2(7)(3)  2(3)(2)  82 in.2
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Volume of Surface Area of a Cube
The volume V and surface area S of a cube
with edge of length s is given by the
formulas
V  s and S  6s .
3
2
s
s
s
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Example: Volume of Surface Area of a
Cube
Find the volume and surface area of the
cube below.
Solution
V  5 =125 ft.
3
5 ft.
3
S  6(5) 2  150 ft.2
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Volume of Surface Area of a Right
Circular Cylinder
The volume V and surface area S of a right
circular cylinder with base radius r and
height h is given by the formulas
V   r h and S  2 rh  2 r .
2
2
h
r
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Example: Volume of Surface Area of a
Right Circular Cylinder
Find the volume and surface area of the
cylinder below.
10 m
Solution
V   (2)2 (10)  40  125.6 m3
2m
S  2 (2)(10)  2 (2)  48  150.72 m
2
2
9-5-16
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Volume of Surface Area of a Sphere
The volume V and surface area S of a
sphere radius r is given by the formulas
4 3
V   r and S  4 r 2 .
3
r
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Example: Volume of Surface Area of a
Sphere
Find the volume and surface area of the
sphere below.
9 in.
Solution
4
3
3
V   (9)  972  3052.08 in.
3
S  4 (9)2  324  1017.36 in.2
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Volume of Surface Area of a Right
Circular Cone
The volume V and surface area S of a right
circular cone with base radius r and height
h is given by the formulas
1 2
2
2
2
V   r h and S   r r  h   r .
3
h
r
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Example: Volume of Surface Area of a
Right Circular Cone
Find the volume and surface area
of the cone below.
4m
3m
Solution
1
V   (3) 2 (4)  12  37.68 m3
3
S   (3) (3) 2  (4) 2   (3) 2  24  75.36 m 2
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Volume of a Pyramid
The volume V of a pyramid with height h
and base of area B is given by the formulas
1
V  Bh.
3
h
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Example: Volume of a Pyramid
Find the volume and surface area of the
pyramid (rectangular base) below.
7 cm
Solution
B  lw  6(3)  18
1
3
V  (18)(6)  36 cm
3
3 cm
6 cm
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