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Chapter 12: Surface Area and Volume of Solids

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## Chapter 12: Surface Area and Volume of Solids

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**Polyhedron**• A solid that is bounded by polygons, called faces, that enclose a single region of space. • Plural is polyhedral or polyhedrons**Face**• One of the flat surfaces that make a polyhedron.**Edge**• A line segment formed by the intersection of two faces of a polyhedron.**Vertex**• A point where three or more edges of a polyhedron meet.**Base**• One of two congruent faces of a polyhedron**Regular Polyhedron**• A convex polyhedron in which all of the faces are congruent regular polygons.**Convex Polyhedron**• A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron. If this segment goes outside the polyhedron, then the polyhedron is nonconvex or concave. convex concave**Platonic Solids**• A convex polyhedron where every face is an identical regular polygon**Tetrahedron**• A polyhedron with four faces**Cube**• A polyhedron with six congruent square faces**Octahedron**• A polyhedron with eight faces**Dodecahedron**• A polyhedron with twelve faces**Icosahedron**• A polyhedron with twenty faces**Cross Section**• The intersection of a plane and a solid**Prism**• A polyhedron with two congruent faces called bases that lie in parallel planes.**Lateral Faces**• The faces of a prism that are parallelograms formed by connecting the corresponding vertices of the bases of the prism**Lateral Edges**• The segments connecting the corresponding vertices of the bases of a prism**Surface Area**• The sum of the areas of the faces of a polyhedron or other solid**Lateral Area**• The sum of the areas of the lateral faces of a polyhedron or other solid with one or two bases.**Net**• The two-dimensional representation of the faces of a polyhedron**Right Prism**• A prism in which each lateral edge is perpendicular to both bases**Oblique Prism**• A prism with lateral edges that are NOT perpendicular to the bases**Cylinder**• A solid with congruent circular bases that lie in parallel planes**Right Cylinder**• A cylinder in which the segment joining the centers of the bases is perpendicular to both bases**Pyramid**• A polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex**Vertex of a Pyramid**• The common vertex of the triangles which make up the lateral faces of a pyramid.**Regular Pyramid**• A pyramid that has a regular polygon for a base and in which the segment joining the vertex and the center of the base is perpendicular to the base**Slant Height**• The height of a lateral face of the regular pyramid**Cone**• A solid that has one circular base and a vertex that is not in the same plane as the base**Vertex of a Cone**• The vertex that does not lie in the same plane as the base of a cone**Right Cone**• A cone in which the segment joining the vertex and the center of the base is perpendicular to the base. The slant height is the distance between the vertex and a point on the base edge.**Lateral Surface**• Consists of all segments that connect the vertex with points on the edge of the base.**Volume**• The number of cubic units contained in the interior of a solid**Sphere**• The set of all points in space equidistant from a given point called the center of the sphere**Center**• The center of a polygon’s circumscribed circle**Radius**• A segment whose endpoints are the center of the circle and a point on the circle. The distance from the center of a circle to any point on the circle. • Plural is radii**Chord**• A segment whose endpoints are on a sphere**Diameter**• A chord that contains the center of a sphere**Great Circle**• The intersection of a sphere and a plane that contains the center of the sphere**Hemisphere**• Half of a sphere, formed when a great circle separates into two congruent halves**Similar Solids**• Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii