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57 terms

Chapter 12 Vocabulary

Mrs. Klaus
STUDY
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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 plan 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
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
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
Volume of a Cube
the volume of a cube is the cube of the length of its sides, or V=s³
Volume Congruence Postulate
If two polyhedral 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
Euler's Theorem
F+V=E+2
Surface Area of a Right Prism
The surface are S of a right prism is S=2B+Ph= aP+Ph, where a is the apothem of the base, B is the area of a base, P is the perimeter of a base, and h is the height.
Surface Area of a Right Cylinder
The surface area S of a right cylinder is S=2B+Ch=2πr²+2 πrh, where B is the area of a base, C is the circumference of a base, r is the radius of a base, and h is the height
Surface Area of a Regular Pyramid
The surface area S of a regular pyramid is S=B+1/2Pl, where B is the area of the base, P is the perimeter of the base, and l is the slant height
Surface Area of a Right Cone
The surface area S of a right cone is S=B+1/2Cl = πr² = πrl, where B is the area of the base, r is the radius of the base, and l is the slant height
Volume of a Prism
The volume V of a prism is V=Bh where B is the area of a base and h is the height.
Volume of a Cylinder
The volume V of a cylinder is V=Bh=πr²h, where B is the area of a base, h is the height, and r is the radius of a base
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 Pyramid
The volume V of a pyramid is V=⅓Bh, where B is the area of the base and h is the height
Volume of a Cone
The volume V of a cone is V=⅓Bh = ⅓πrh, where B is the area of the base, h is the height, and r is the radius of the base
Surface Area of a Sphere
The surface area S of a sphere with radius r is S=4πr²
Volume of a Sphere
The volume V of a sphere with radius r is 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