1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Solve. Use 3.14 as an estimate 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?
 cm
3. Find the area of a circle with a 12 ft
radius.
 ft2

3. 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

4. Vocabulary
polyhedron
face
edge
vertex
cube
base

5. 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.

6. 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

7. 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

8. Two types of polyhedrons are prisms and pyramids
Two 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.

9. The bottom face of a prism is not always one of its bases
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

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

12. Additional Example 2A: Naming Three-Dimensional 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.

13. Additional Example 2B: Naming Three-Dimensional 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.

14. Additional Example 2C: Naming Three-Dimensional 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.

15. 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.

16. 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.

17. 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.

18. Lesson 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
8 faces, 18 edges, and 12 vertices
cylinder
cone