LESSON 49 Introduction to Solids

VOCABULARY Solids are three-dimensional figures that have flat and/or curved surfaces Polyhedron is a closed solid formed by four or more polygons that intersect only at their edges Cone is a solid with a circular base and a curved lateral face that comes to a point Cylinder is a solid with two parallel congruent circular bases and a curved lateral face that connects the bases Sphere is a set of points in space that are a fixed distance from a given point, called the center of the sphere

MORE VOCABULARY OF SOLIDS Each flat surface (polygons) of a polyhedron is called the face of the polyhedron The segment that is the intersection of two faces of a solid is the edge The vertex of a polyhedron is the point of intersection of three or more faces (plural is vertices) A diagonal of a polyhedron is a segment whose endpoints are the vertices of two different faces

TYPES OF POLYHEDRONS A prism is a polyhedron formed by two parallel congruent polygonal bases connected by lateral faces that are parallelograms bb ase of a prism is one of the two congruent parallel faces ll ateral face is a face that is not a base A pyramid is a polyhedron formed by a polygonal base and triangular lateral faces that meet at a common vertex opposite the base

PRISMS AND PYRAMIDS ARE NAMED BY THE SHAPE OF THEIR BASES

REGULAR POLYHEDRONS/PRISMS/PYRAMIDS A polyhedron is regular if all of its faces are congruent, regular polygons A prism is regular if its bases are regular polygons and its lateral faces are rectangles A pyramid is regular if its base is a regular polygon and its lateral faces are congruent isosceles triangles 1. W hat is a common characteristic of regular polyhedrons, regular prisms, and regular pyramids? All three contain at least one regular polygonal face 2. I s a cube a regular prism or regular polyhedron? A cube is both a regular prism and regular polyhedron since all six faces are squares

EULER’S FORMULA

APPLICATION: DIAMOND CUTTING Diamonds are cut to change them from a rough stone to a gemstone. The triangular pyramid below shows the finished product after each vertex is cut. What is the number of faces, edges, and vertices on the gemstone? Verify your answer. 1.How many faces, edges, and vertices does a triangular pyramid have? 4 faces, 6 edges, 4 vertices

LOOKING FORWARD Working with solids will prepare you for: II nvestigation 5: Nets LL esson 54: Representing Solids LL esson 59: Finding Surface Areas and Volumes of Prisms LL esson 62: Finding Surface Areas and Volumes of Cylinder LL esson 70: Finding Surface Areas and Volumes of Pyramids LL esson 77: Finding Surface Areas and Volumes of Cones LL esson 80: Finding Surface Areas and Volumes of Spheres LL esson 85: Cross Sections of Solids LL esson 93: Representing Solids with Orthographic Views LL esson 99: Volume Ratios of Similar Solids