Preview Warm Up California Standards Lesson Presentation

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?  56.52 cm 3. Find the area of a circle with a 12 ft radius.  452.16 ft2

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

Vocabulary polyhedron face edge vertex cube base

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.

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

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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