10-6 Three-Dimensional Figures

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

10-6 Three-Dimensional Figures

2. The radius of a circle is 9 cm. What is its circumference?

1. The diameter of a circle is 12 in. What is the circumference?

Warm UpSolve. Use 3.14 for .

37.68 in.

56.52 cm

452.16 ft2

3. Find the area of a circle with a 12 ftradius.

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

10-6 Three-Dimensional Figures

Learn to name three-dimensional figures.

10-6 Three-Dimensional Figures

Vocabulary

polyhedron cylinderface pyramidedge conevertex sphereprismbase

10-6 Three-Dimensional Figures

A polyhedron is a three-dimensional object with flat surfaces, called faces, that are polygons.

When two faces of a three-dimensional figure share a side, they form an edge. A point at which three or more edges meet is a vertex (plural: vertices).

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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.

A.

B.

5 faces

8 edges

5 vertices

7 faces

15 edges

10 vertices

10-6 Three-Dimensional Figures

Check It Out: Example 1

Identify the number of faces, edges, and vertices on each three-dimensional figure.

A.

B.

6 faces

12 edges

8 vertices

5 faces

9 edges

6 vertices

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.

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10-6 Three-Dimensional Figures

A pyramid has one polygon-shaped base and three or more triangular faces that share a vertex. 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 sphere has no base and one curved surface. All points on the surface are the same distance from a point called the center of the sphere.

10-6 Three-Dimensional Figures

Cones and spheres are not polyhedrons because they have curved surfaces.

Helpful Hint

10-6 Three-Dimensional Figures

Additional Example 2A: Naming Three-Dimensional Figures

Name the three-dimensional figure represented by the object.

The figure is not a polyhedron.

There is a curved surface.

The figure represents a cylinder.

There are two congruent, parallel bases.

The bases are circles.

10-6 Three-Dimensional Figures

Additional Example 2B: Naming Three-Dimensional Figures

Name the three-dimensional figure represented by the object.

The figure is a polyhedron.

All the faces are flat and are polygons.

The figure is a triangular pyramid.

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.

10-6 Three-Dimensional Figures

Additional Example 2C: Naming Three-Dimensional Figures

Name the three-dimensional figure represented by the object.

The figure is a polyhedron.

All the faces are flat and are polygons.

The figure is a rectangular prism.

There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles.

10-6 Three-Dimensional Figures

Check It Out: Example 2A

Name the three-dimensional figure represented by the object.

The figure is a polyhedron.

All the faces are flat and are polygons.

The figure is a square pyramid.

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.

10-6 Three-Dimensional Figures

Check It Out: Example 2B

Name the three-dimensional figure represented by the object.

The figure is a polyhedron.

All the faces are flat and are polygons.

The figure is a rectangular prism.

There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles.

10-6 Three-Dimensional Figures

Check It Out: Example 2C

Name the three-dimensional figure represented by the object.

The figure is not a polyhedron.

There is a curved surface.

The figure represents a cylinder.

There are two congruent, parallel bases.

The bases are circles.

10-6 Three-Dimensional Figures

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

10-6 Three-Dimensional Figures

Lesson Quiz

1. Identify the number of faces, edges, and vertices in the figure shown.

Identify the figure described.

2. two congruent circular faces connected by a

curved surface

3. one flat circular face and a curved lateral

surface that comes to a point

cylinder

8 faces, 18 edges, and 12 vertices

cone

10-6 Three-Dimensional Figures

1. Identify the number of faces, edges, and vertices in the figure shown.

A. 9 faces, 21 edges, and 14 vertices B. 21 faces, 9 edges, and 14 verticesC. 9 faces, 14 edges, and 21 verticesD. 21 faces, 14 edges, and 9 vertices

Lesson Quiz for Student Response Systems

10-6 Three-Dimensional Figures

2. Identify the figure described. A square base with four triangles that come to a point.

A. square prism B. square pyramid C. rectangular prismD. rectangular pyramid

Lesson Quiz for Student Response Systems

10-6 Three-Dimensional Figures

3. Identify the figure described. A hexagonal base with six triangles that come to a point.

A. hexagonal prism B. triangular prism C. hexagonal pyramid D. triangular pyramid

Lesson Quiz for Student Response Systems