Chapter 12 vocabulary

Lateral area of a cylinder

The area of the curved surface of a cylinder.

Cross Section

The intersection of a plane and a solid.

Great circle

The intersection of a sphere and a plane that contains the center of the sphere.

Center of a sphere

The locus of points in space that are a given distance from a point, the point is called the center of the sphere.

Sphere

The locus points in space that are a given distance from a point, called the center of the sphere.

Volume of a solid

The number of cubic units contained in its interior.

Platonic Solids

five regular polyhedra, named after the Greek mathematician and philosopher plato, including a regular tetrahedron, a cube, a regular octahedron, a regular dodecahedron, and a regular icosahedron.

Similar Solids

two solids with equal ratios of corresponding linear measures, such as heights or radii.

Right cone

A cone with a vertex that lies directly above the center of the base. The slant height of a right cone is the distance between the vertex and a point on the edge of the base.

Right cylinder

A cylinder such that the segment joining the centers of the bases is perpendicular to the bases.

Edge

A line segment formed by the intersection of two faces of a polyhedron.

Pyramid

A polyhedron in which the base is a common polygon and the lateral faces are triangles with a common vertex. The intersection of 2 lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge. The altitude or height is the perpendicular distance between the base and the vertex.

Lateral area of a polyhedron

A polyhedron is the sum of the areas of its lateral faces.

Lateral surface of a cone

Consists of all segments that connect the vertex with points on the base edge.

Bases of a prism

2 congruent faces on a polyhedron, called bases, that lie in parallel planes.

Net

A 2-dimensional representation of all faces of a polyhedron.

Dodecahedron

A polyhedron with 12 faces.

Prism

A polyhedron with 2 congruent faces, called bases, that lie in parallel planes. The other faces, called lateral faces, are parallelograms formed by connecting the corresponding vertices of the bases. The segments connecting the vertices are lateral edges. The altitude or height of a prism is the perpendicular distance between its bases.

Icosahedron

A polyhedron with 20 faces.

Tetrahedron

A polyhedron with 4 faces.

Octahedron

A polyhedron with 8 faces.

Oblique prisms

A prism whose lateral edges are not perpendicular to the bases. The length of the oblique lateral edges is the slant height of the prism.

Right prism

A prism whose lateral edges are perpendicular to both bases.

Regular pyramid

A pyramid such that the base is a regular polygon and the segment from the vertex to the center of the base is perpendicular to the base. In a regular pyramid, the lateral faces all have the same slant height.

Radius of a sphere

A segment from the center of a sphere to a point on the sphere. The length of a segment from the center of a sphere to a point on the sphere.

Chord of a sphere

A segment whose endpoints are on the sphere.

Polyhedron

A solid that is bounded by polygons, called faces, that enclose a single region of space.

Faces

A solid that is bounded by polygons.

Circular Cone

A solid with a circular base and a vertex that is not in the same plane as the base. The lateral surface consists of all segments that connect the vertex with points on the edge of the base. The altitude or height is the perpendicular distance between the vertex and the plane that contains the base.

Cylinder

A solid with congruent circular bases that lie in parallel planes. The altitude or height of a cylinder is the perpendicular distance between its bases. The radius of the base is also called the radius of the cylinder.

Hemispheres

Half os a sphere, formed when a great circle separates a sphere into 2 congruent halves.

Lateral faces of a prism

Parallelograms formed by connecting the corresponding vertices of the bases.

Suface area of a polyhedron

The sum of the areas of its faces.

Surface area of a cylinder

The sum of the lateral area of the cylinder and the areas of the 2 bases.