Holt CA Course 1

10-7 Three-Dimensional Figures

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Holt CA Course 1

10-7 Three-Dimensional Figures

Warm UpSolve. Use 3.14 as an estimate for .

37.68 in.

56.52 cm

452.16 ft2

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

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

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

Holt CA Course 1

10-7 Three-Dimensional Figures

Preparation for MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.

California Standards

Holt CA Course 1

10-7 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).

A cube is formed by 6 congruent square faces. It has 8 vertices and 12 edges.

Holt CA Course 1

10-7 Three-Dimensional FiguresTwo types of polyhedrons are prisms and pyramids. Prisms and pyramids are named for the shape of their bases. A base of a three-dimensional figure is a face by which the figure is measured or classified.

Holt CA Course 1

10-7 Three-Dimensional Figures

The bottom face of a prism is not always one of its bases. For example, the bottom face of the triangular prism in Example 1 is not one of its triangular bases.

Helpful Hint

Holt CA Course 1

10-7 Three-Dimensional Figures

Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because their surfaces are not polygons.

Holt CA Course 1

10-7 Three-Dimensional Figures

Holt CA Course 1

10-7 Three-Dimensional Figures

Vocabularypolyhedronfaceedgevertexcubebase

Holt CA Course 1

10-7 Three-Dimensional FiguresAdditional 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

Holt CA Course 1

10-7 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.

Holt CA Course 1

10-7 Three-Dimensional FiguresAdditional 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.

Holt CA Course 1

10-7 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

Holt CA Course 1

10-7 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.

Holt CA Course 1

10-7 Three-Dimensional FiguresLesson Quiz

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

Identify the figure described

2. two parallel 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

Holt CA Course 1

10-7 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.

Holt CA Course 1

10-7 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.

Holt CA Course 1

10-7 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.