# Chapter 12 VPTF

## 57 terms

### Polyhedron

a solid bounded by polygons called faces

### Face (of a Polyhedron)

polygons that bound a polyhedron

### Edge (of a Polyhedron)

Line Segment formed by the intersection of two faces

### Vertex (of a Polyhedron)

point where three or more edges meet

### Base

used to name a prism or pyramid

### Regular Polyhedron

all faces are congruent regular polygons

### Convex Polyhedron

any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron

### Platonic Solids

the five regular polyhedral

### Tetrahedron

4 faces (Platonic Solid)

### Cube

6 faces (Platonic Solid)

### Octahedron

8 faces (Platonic Solid)

### Dodecahedron

12 faces (Platonic Solid)

### Icosahedron

20 faces (Platonic Solid)

### Cross Section

intersection of the plane and the solid

### Prism

polyhedron with two congruent faces, called bases that lie in parallel planes

### Lateral Faces

parallelograms formed by connecting the corresponding vertices of the bases

### Lateral Edges

segments connecting the vertices of the lateral faces

### Surface Area (of a Polyhedron)

the sum of the areas of its faces

### Lateral Area (of a Polyhedron)

the sum of the areas of its lateral faces

### Net

two-dimensional representation of the faces

### Right Prism

each lateral edge is perpendicular to both bases

### Oblique Prism

a prism with lateral edges that are not perpendicular to the bases

### Cylinder

solid with congruent circular bases that lie in parallel planes

### Right Cylinder

segment joining the centers of the bases is perpendicular to the 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 in a pyramid

### Regular Pyramid

has a regular polygon for a base and the segment joining the vertex and the center of the base is perpendicular to the base

### Slant Height (of a Regular Pyramid)

the height of a lateral face of the regular pyramid

### Cone

has a circular base

### Vertex (of a Cone)

not in the same plane as the base

### Right Cone

the segment joining the vertex and the center of the base is perpendicular to the base, and the slant height is the distance between the vertex and a point on the base edge

### Lateral Surface (of a Cone)

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

### Volume (of a Solid)

the number of cubic units contained in its interior

### Sphere

the set of all points in space equidistant from a given point

### Center (of a Sphere)

point the set of all points of a Sphere are equidistant from

a segment from the center to a point on the sphere

### Chord (of a Sphere)

a segment whose endpoints are on the sphere

### Diameter (of a Sphere)

a chord that contains the center

### 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 a sphere into two congruent halves

### Similar Solids

two solids of the same type with equal ratios of corresponding linear measures, such as height or radii

V=s³

### Volume Congruence Postulate

If two polyhedral are congruent, then they have the same volume

The volume of a solid is the sum of the volumes of all its non-overlapping parts

F+V=E+2

### Surface Area of a Right Prism

S=2B+Ph or (aP+Ph)

### Surface Area of a Right Cylinder

S=2B+Ch or (2πr²+2πrh)

S=B+1/2Pl

### Surface Area of a Right Cone

S=B+1/2Cl or (πr² +2πrl)

V=Bh

V=Bh or (πr²h)

### Cavalieri's Principle

If two solids have the same height and the same cross-sectional area at every level, then they have the same volume

V=⅓Bh

V=⅓Bh or (⅓πrh)

S=4πr²

V=4/3πr³

### Similar Solids Theorem

If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a²:b², and corresponding volumes have a ration of a³:b³