The document provides information about geometric shapes in three dimensions including polyhedrons, cylinders, pyramids, cones, spheres, prisms, and identifying their key features such as faces, edges, and vertices. It gives examples of naming different three-dimensional figures based on descriptions of their properties and includes practice problems and quizzes for students.

1. Warm Up Lesson Presentation Problem of the Day Lesson Quizzes

2. 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 Up Solve. Use 3.14 for  . 37.68 in. 56.52 cm 452.16 ft 2 3. Find the area of a circle with a 12 ft radius.

3. 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

4. Review of MA.5.G.3.1 Analyze and compare the properties…of three-dimensional solids (polyhedra)… Also Prep for MA.6.G.4.3 Sunshine State Standards

5. Vocabulary polyhedron cylinder face pyramid edge cone vertex sphere prism base

6. 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 ).

7. 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

8. 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

9. 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.

10. 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.

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

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. 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

20. 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 vertices C. 9 faces, 14 edges, and 21 vertices D. 21 faces, 14 edges, and 9 vertices Lesson Quiz for Student Response Systems

21. 2. Identify the figure described. A square base with four triangles that come to a point. A. square prism B. square pyramid C. rectangular prism D. rectangular pyramid Lesson Quiz for Student Response Systems

22. 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