Chapter 12: Surface Area and Volume of

Solids

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

Stop for today.

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