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