Surface Area & Volume
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Transcript Surface Area & Volume
Chapter 12
Section 12-1
Also
called solids
Enclose part of space
Solids
with flat surfaces
that are polygons
Faces
– 2-dimensional
surfaces formed by
polygons
Edge – where 2 faces
intersect
Vertex – the point where 3
or more edges intersect
Two parallel faces called
bases that are congruent
polygons
Other faces are called
lateral faces
Lateral faces intersect in
lateral edges
All faces except the base
intersect at the vertex
The triangular faces that
meet at the vertex are
called lateral faces
The
two bases are
congruent, parallel
circles
The lateral surface is
curved
The
base is a circle
The lateral surface is
curved
The point is called the
vertex
Section 12-2
Lateral
Area - The sum of
the areas of its lateral faces
Surface Area – The sum of
the areas of all its surfaces
Lateral
L
Area of a Prism
= Ph
P= perimeter of the base
h= height of the prism
Surface
Area of a Prism
S = Ph + 2b
B = area of the base
Lateral
Area of a
Cylinder
L = 2 rh
r = radius of the base
h= height of the cylinder
Surface
Area of a Cylinder
2
S = 2 rh + 2 r
Section 12-3
The
measurement of the
space contained within a
solid figure
Volume
V
of a Prism
= Bh
B = area of the base
h = height of the prism
Volume of
2
V = r h
r
a Cylinder
= radius of the base
h = height of the cylinder
Section 12-4
The
segment from the vertex
perpendicular to the base
In a right pyramid or cone, the
altitude is perpendicular to the
center
In an oblique pyramid or cone,
the altitude is perpendicular at
another point
A right pyramid whose
base is a regular polygon
The
height of each
lateral face of a pyramid
Represented by l
Lateral
Area of a Regular
Pyramid
L = ½ Pl
P = perimeter of the base
l = slant height
Surface
Area of a Regular
Pyramid
S = ½ Pl + B
B = area of the base
Lateral Area of a Cone
L = rl
r = radius of the base
l = slant height of the
cone
Surface Area of a Cone
2
S = rl + r
Section 12-5
Volume
of a Pyramid
V = 1/3Bh
B = area of the base
h = height of the pyramid
Volume
of a Cone
2
V = 1/3 r h
r = radius of the base
h = height of the cone
Section 12-6
A
sphere is a set of all
points that are a given
distance from a given
point called the center.
A line that intersects the
sphere at exactly one
point
Surface Area of a Sphere
2
S = 4 r
r = radius of the sphere
Volume of a Sphere
3
V = 4/3 r
Section 12-7
For
similar solids, the
corresponding lengths are
proportional, and the
corresponding faces are
similar.
If two solids are similar
with a scale factor of a:b,
then the surface areas
2
2
have a ratio of a :b and
the volumes have a ratio
of a3:b3