Chapter 12 Geometry

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 polygon and the lateral faces are triangles with a common vertex. The intersection of two 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.

convex

A polyhedron such that any two points on its surface can be connected by a line segment that lies entirely inside or on the polyhedron. If this line goes outside the polyhedron, then the polyhedron is nonconvex, or concave.

regular polyhedron

A polyhedron whose faces are all congruent regular polygons.

octahedron

A polyhedron with eight faces.

tetrahedron

A polyhedron with four faces.

dodecahedron

A polyhedron with twelve faces.

icosahedron

A polyhedron with twenty faces.

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 the sphere to a point on the sphere

polyhedron

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

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.

net

A two-dimensional representation of all the faces of a polyhedron.

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.

lateral area of a cylinder

The area of the curved surface of a cylinder.

cross section

The intersection of a plane, and a solid.

sphere

The locus of 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 the interior of a solid

surface area of a polyhedron

The sum of the areas of its faces.

lateral area of a polyhedron

The sum of the areas of the lateral faces of a polyhedron.

surface area of a cylinder

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

similar solids

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

diameter of a sphere

a chord that contains the center

vertex

a point where three or more edges meet

chord of a sphere

a segment whose endpoints are on the sphere

face

bounds a polyhedron, enclose an individual/single region of space

lateral surface of a cone

consists of all segments that connect the vertex with points on the base edge, when you cut along the slant height and lie the cone flat, you get the net shown at the right. In the net, the circular base has an area of pi x radius squared and the lateral surface is the sector of a circle. you can find the area of this sector by using a proportion, as shown below.

lateral faces

faces of a polyhedron; they're parallelograms formed by connecting the corresponding vertices of the bases

hemisphere

half of a sphere (sphere was separated into two congruent halves called ______)

center of a sphere

the middle point of a sphere

great circle

the pane intersected contains the center of the sphere

bases

the part of a polyhedron with two congruent faces that lie in parallel planes

prism

A polyhedron with two 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.

oblique prism

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.

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.