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Solid
Geometry
Solid
geometry
is the study of
three-dimensional
shapes
, also known as solids. These
shapes
have
length
,
width
, and
height
, unlike
two-dimensional
shapes
which only have
length
and
width
.
Types of Solids
There are several types of solids that are important to understand in solid
geometry
:1.
Prisms
:
Prisms
are
polyhedra
with two congruent
parallel
bases
and
rectangular faces
. Examples include
rectangular prisms
,
triangular prisms
, and
hexagonal prisms
.2.
Pyramids
:
Pyramids
have a polygonal
base
and
triangular faces
that meet at a common
point
called the apex. Examples include
square pyramids
,
triangular pyramids
, and
pentagonal pyramids
.3.
Cylinders
:
Cylinders
have two congruent
parallel
bases
that are
circles
and a curved surface. Examples include circular
cylinders
and elliptical
cylinders
.4.
Cones
:
Cones
have a circular
base
and a curved surface that tapers to a
point
called the apex.5.
Spheres
:
Spheres
are
three-dimensional
shapes
that are perfectly round, like a ball.
Formulas
for Solids
To work with solids, it's important to understand the
formulas
for their
surface area
and
volume
.1.
Surface Area
:
- For a
Prism
: 2 *
base
area
+
perimeter
of
base
* height - For a
Cylinder
: 2 * π *
radius
* (
radius
+
height
) - For a
Pyramid
:
base
area
+ 1/2 *
perimeter
of
base
* slant height - For a
Cone
: π *
radius
* (
radius
+
slant height
) - For a
Sphere
: 4 * π * radius^22.
Volume
:
- For a
Prism
:
base
area
* height - For a
Cylinder
: π * radius^2 * height - For a
Pyramid
: 1/3 *
base
area
* height - For a
Cone
: 1/3 * π * radius^2 * height - For a
Sphere
: 4/3 * π * radius^3
Study Guide
[Solid] Related Worksheets and Study Guides:
Solids and Faces
Mathematics • Third Grade
Solids
Mathematics • Second Grade
Solids, liquids and gases
Science • Sixth Grade
.
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Select and use appropriate statistical methods to analyze data.
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