chapter 12: surface area and volume of solids. polyhedron a solid that is bounded by polygons,...
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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
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