1. A. Polyhedrons 1. Vocabulary of Polyhedrons 2. Building Polyhedrons a. Create a net from the Polyhedron b. Create the Polyhedron from the net B. Prisms and Cylinders 1. Right Prism – Cylinder 2. Oblique Prism – Cylinder C. Pyramids and Cones 1. Right Pyramid – Cone 2. Oblique Pyramid - Cone D. Spheres 1. Terminology 2. Volume E. Proportions with Volume F. Applications in the Real-World ESSENTIAL CONTENT

3. LESSON OBJECTIVES Learn the vocabulary of polyhedrons—prisms and pyramids in particular Learn the vocabulary of spheres, cylinders, and cones Practice three-dimensional visual thinking skills

4. Most of the geometric figures you have worked with so far have been flat plane figures with two dimensions: base and height

5. In this chapter you will work with solid figures with three dimensions— length, width, and height. Solid Geometry is the geometry of three- dimensional space, the kind of space we live in

6. Most real-world solids, like rocks and plants, are very irregular, but many others are geometric. Some real-world geometric solids occur in nature: viruses, oranges, crystals, the earth itself. Others are human made: books, buildings, baseballs, soup cans, ice cream cones.

9. Volume (think of how much water it could hold) Surface area (think of the area you would have to paint) Vertices (corner points), faces and edges they have Solids properties

10. Types of Solids There are two main types of solids: Polyhedra (they must have flat faces) Non-Polyhedra: if any surface is not flat https://www.youtube.com/watch?v=yq7VTjoMYVk

11. POLYHEDRONS

12. A solid formed by polygons that enclose a single region of space POLYHEDRON. The flat polygonal surfaces of a polyhedron. Although a face of a polyhedron includes the polygon and its interior region, we identify the face by naming the polygon that encloses it FACES Segment where two faces intersect EDGE The point of intersection of three or more edges VERTEX OF THE POLYHEDRON.

14. The plural of polyhedron is either polyhedrons or polyhedra.

15. How is a polyhedron classified? Just as a polygon is classified by its number of sides, a polyhedron is classified by its number of faces The prefixes for polyhedrons are the same as they are for polygons with one exception: A polyhedron with four faces is called a tetrahedron. The name may not describe the figure other than by the number of faces. For example, the prefix hex- means “six,” and a hexahedron may be a pyramid or a prism or some other figure

16. Here are some examples Hexahedrons Heptahedrons Decahedrons

17. Regular polyhedron A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons arranged all in exactly the same way around each vertex. Regular dodecahedron because it has 12 faces.

18. SPECIAL TYPES OF POLYHEDRON Prism and Pyramid

19. It is a special type of polyhedron, with two faces called bases, that are congruent, parallel polygons. The other faces of the polyhedron, called lateral faces, are parallelograms that connect the corresponding sides of the bases. The lateral faces meet to form the lateral edges.

20. How is PRISM classified? Prisms are classified by their bases. For example, a prism with triangular bases is a triangular prism, and a prism with hexagonal bases is a hexagonal prism. Rectangular prismtriangular prism http://www.mathopenref.com/prism.html

21. A prism whose lateral faces are rectangles is called a right prism A prism that is not a right prism is called an oblique prism. How is PRISM classified?

22. The altitude of a prism It is any perpendicular segment from one base to the plane of the other base. The height of the prism. It is the length of an altitude

24. Pyramids have only one base. As in a prism, the other faces are called the lateral faces, and they meet to form the lateral edges. The common vertex of the lateral faces is the vertex of the pyramid. The altitude of the pyramid is the perpendicular segment from its vertex to the plane of its base. The length of the altitude is the height of the pyramid. http://www.mathopenref.com/pyramid.html

25. How is a PYRAMID classified? Like prisms, pyramids are also classified by their bases Triangular pyramid Square pyramid Trapezoidal pyramid Hexagonal pyramid http://www.mathopenref.com/pyramid.html

26. GEOMETRIC SOLIDS THAT HAVE CURVED SURFACES. Cylinder- cone - sphere

27. A cylinder has two bases that are both parallel and congruent. The bases of cylinders are circles. If you were to 'unroll' the cylinder you would find the side is actually a rectangle when flattened out. The segment connecting the centers of the bases is called the axis of the cylinder. The radius of the cylinder is the radius of a base.

28. The altitude of a cylinder is any perpendicular segment from the plane of one base to the plane of the other. The height of a cylinder is the length of an altitude.

29. Right cylinderOblique cylinder http://www.mathsisfun.com/geometry/cylinder.html http://www.mathopenref.com/cylinder.html http://www.mathopenref.com/cylinderoblique.html

30. A cone has a base and a vertex. The base of a cone is a circle and its interior. The radius of a cone is the radius of the base. The vertex of a cone is the point that is the greatest perpendicular distance from the base. The altitude of a cone is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height of a cone.

31. If the line segment connecting the vertex of a cone with the center of its base is perpendicular to the base, then the cone is a right cone. Right coneOblique cone http://www.mathopenref.com/cone.html

32. A sphere is the set of all points in space at a given distance from a given point. The given distance is called the radius of the sphere, and the given point is the center of the sphere http://www.mathopenref.com/spherevolume.html

33. A hemisphere is half a sphere and its circular base. The circle that encloses the base of a hemisphere is called a great circle of the sphere. Every plane that passes through the center of a sphere determines a great circle.

34. Building Polyhedrons

35. http://www.mathsisfun.com/geometry/polyhedron-models.html The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain uniformity of distribution conditions, and a topological generalization of a sequence. The net of a polyhedron is also known as a development, pattern, or planar net The net of a polyhedron must in general also specify which edges are to be joined

36. http://www.mathsisfun.com/geometry/polyhedron-models.html net for the cube. net for the tetrahedron. http://www.enchantedlearning.com/math/geometry/solids/