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polyhedron

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

edge

an edge of a polyhedron is a line segment formed by the intersection of two faces

vertex

a vertex of a polyhedron is a point where three or more edges meet

regular

if a polyhedron is regular if all of its faces are congruent regular polygons

convex

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

cross section

the of intersection of a plane and a solid

platonic solids

-tetrahedron (4 faces)

-octahedron (8 faces)

-dodecahedron (12 faces)

-icosahedron (20 faces)

-octahedron (8 faces)

-dodecahedron (12 faces)

-icosahedron (20 faces)

Euler's Theorem

F + V = E + 2

surface area

SA= LA + 2B

Volume Congruence Postulate

if two polyhedra are congruent, then they have the same volume

Volume Addition Postulate

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

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

volume of a prism or cylinder

V=Bh

volume of a pyramid or cone

V=(1/3)Bh

sphere

the locus of points in space that are a given distance from a point (center of the sphere)

radius of a sphere

a segment from the center to a point on the sphere

chord of a sphere

a segment whose endpoints are on the sphere

similar solids

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

Similar Solids Theorem

if two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a^2:b^2, and corresponding volumes have a ratio of a^3:b^3