10-6 Three-Dimensional Figures
Warm Up
Problem of the Day
Lesson Presentation
Course 1
10-6 Three-Dimensional Figures
Warm Up
Solve. Use 3.14 for .
1. The diameter of a circle is 12 in. What is
the circumference? 37.68 in.
2. The radius of a circle is 9 cm. What is
its circumference? 56.52 cm
3. Find the area of a circle with a 12 ft
radius. 452.16 ft2
Course 1
10-6 Three-Dimensional Figures
Problem of the Day
To measure the perimeter of her square
patio, Becky used an old bicycle wheel
with a 22 in. diameter. She rolled the
wheel from one corner of the patio
along the edge to the next. The wheel
made 6.75 revolutions. What is the
perimeter in feet of the patio? Use 3.14
for .
155.43 ft
Course 1
10-6 Three-Dimensional Figures
Learn to name three-dimensional figures.
Course 1
10-6 Three-Dimensional
Insert Lesson Title Figures
Here
Vocabulary
polyhedron
face
edge
vertex
prism
base
pyramid
cylinder
cone
Course 1
10-6 Three-Dimensional Figures
A polyhedron is a three-dimensional
object, or solid figure, with flat surfaces,
called faces, that are polygons.
When two faces of a three-dimensional
figure share a side, they form an edge.
On a three-dimensional figure, a point at
which three or more edges meet is a
vertex (plural: vertices).
Course 1
10-6 Three-Dimensional Figures
Additional Example 1: Identifying Faces,
Edges, and Vertices
Identify the number of faces, edges, and
vertices on each three-dimensional figure.
5 faces
A.
8 edges
5 vertices
B.
7 faces
15 edges
10 vertices
Course 1
10-6 Three-Dimensional Figures
Check It Out: Example 1
Identify the number of faces, edges, and
vertices on each three-dimensional figure.
6 faces
A.
12 edges
8 vertices
B.
5 faces
9 edges
6 vertices
Course 1
10-6 Three-Dimensional Figures
A prism is a polyhedron with two congruent,
parallel bases, and other faces that are all
parallelograms. A prism is named for the shape of
its bases. A cylinder also has two congruent,
parallel bases, but bases of a cylinder are circular.
A cylinder is not a polyhedron because not every
surface is a polygon.
Course 1
10-6 Three-Dimensional Figures
A pyramid has one polygon shaped base, and the
other faces are triangles that come to a point. A
pyramid is named for the shape of its base. A cone
has a circular base and a curved surface that comes
to a point. A cones is not a polyhedron because not
every surface is a polygon.
Course 1
10-6 Three-Dimensional Figures
Helpful Hint
The point of a cone is called its vertex.
Course 1
10-6 Three-Dimensional Figures
Additional Example 2A: Naming ThreeDimensional Figures
Name the three-dimensional figure
represented by the object.
There is a curved surface.
The figure is not a polyhedron.
There are two congruent, parallel
bases.
The bases are circles.
The figure represents a cylinder.
Course 1
10-6 Three-Dimensional Figures
Additional Example 2B: Naming ThreeDimensional Figures
Name the three-dimensional figure
represented by the object.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There is one base and the other
faces are triangles that meet at a
point, so the figure is a pyramid.
The base is a triangle.
The figure is a triangular pyramid.
Course 1
10-6 Three-Dimensional Figures
Additional Example 2C: Naming ThreeDimensional Figures
Name the three-dimensional figure
represented by the object.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There are two congruent, parallel
bases, so the figure is a prism. The
bases are rectangles.
The figure is a rectangular prism.
Course 1
10-6 Three-Dimensional Figures
Check It Out: Example 2A
Name the three-dimensional figure
represented by the object.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There is one base and the other
faces are triangles that meet at a
point, so the figure is a pyramid.
The base is a square.
The figure is a square pyramid.
Course 1
10-6 Three-Dimensional Figures
Check It Out: Example 2B
Name the three-dimensional figure
represented by the object.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There are two congruent, parallel
bases, so the figure is a prism. The
bases are rectangles.
The figure is a rectangular prism.
Course 1
10-6 Three-Dimensional Figures
Check It Out: Example 2C
Name the three-dimensional figure
represented by the object.
There is a curved surface.
The figure is not a polyhedron.
There are two congruent, parallel
bases.
The bases are circles.
The figure represents a cylinder.
Course 1
10-6 Three-Dimensional
Insert Lesson Title Figures
Here
Lesson Quiz
1. Identify the number of faces, edges, and
vertices in the figure shown.
8 faces, 18 edges, and
12 vertices
Identify the figure described
2. two congruent circular faces connected by a
curved surface cylinder
3. one flat circular face and a curved lateral
surface that comes to a point
Course 1
cone