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Pearson Geometry Common Core Chapter 11
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Gravity
Terms in this set (41)
Polyhedron
A space figure, or three-dimensional figure whose surfaces, or faces, are polygons. The vertices of the polygons are the vertices of the polyhedron. The intersections of the faces are the edges of the polyhedron. (11.1)
Prism
A polyhedron with two congruent, parallel faces, which are called the bases. The other faces are called the lateral faces. (11.2)
Right Prism
A prism whose lateral faces are rectangular regions and a lateral edge is an altitude. (11.2)
Oblique Prism
A prism in which some or all of the lateral faces are non rectangular. (11.2)
Altitude of a Prism or Cylinder
A perpendicular segment that joins the planes of the bases. Its length is the height. (11.2)
Lateral Area of a Prism
LA = ph, p is the perimeter, h is the height. (11.2)
Surface Area of a Prism
SA = LA + 2B, LA is the lateral area and B is the area of the bases. (11.2)
Cylinder
A solid that has two congruent parallel bases that are circles. (11.2)
Right Cylinder
A cylinder in which the segment joining the centers of the bases is an altitude. (11.2)
Oblique Cylinder
A cylinder in which the segment joining the centers of the bases is not perpendicular to the planes containing the bases. (11.2)
Lateral Area of a Cylinder
LA=2πrh, r is the radius, h is the height.
LA=πdh, d is the diameter, h is the height. (11.2)
The resulting rectangle of the 'lateral face'.
Surface Area of a Cylinder
SA = 2πrh+2πr², r is the radius, h is the height. (11.2)
Pyramid
A polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid). (11.3)
Altitude of a Pyramid
The perpendicular segment from the vertex to the plane of the base. (11.3)
Regular Pyramid
A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. (11.3)
Slant Height of a Pyramid
The length of the altitude of a lateral face of the pyramid. (11.3)
Lateral Area of a Pyramid
LA = ½pl, p is the perimeter of the base, l is the slant height. (11.3)
Surface Area of a Pyramid
SA = ½pl + B, p is the perimeter of the base, l is the slant height, B is the area of the base. (11.3)
Cone
A solid that has one base and a vertex that is not in the same plane as the base. (11.3)
Altitude of a Cone
The perpendicular segment from the vertex to the plane of the base. (11.3)
Right Cone
The altitude is a perpendicular segment from the vertex to the center of the base. (11.3)
Slant Height of a Cone
The distance from the vertex to a point on the edge of the base. (11.3)
Lateral Area of a Cone
LA = πrl, r is the radius, l is the slant height. (11.3)
Surface Area of a Cone
SA = πrl+πr², r is the radius, l is the slant height. (11.3)
Volume
The space that a figure occupies. (11.4)
Volume of a Prism
V = Bh, B is the area of the base, h is the height of the cylinder. (11.4)
Volume of a Cylinder
V = Bh, B is the area of the base, h is the height of the cylinder.
V = πr²h, r is the radius, h is the height of the cylinder. (11.4)
Composite Space Figure
A three dimensional figure that is the combination of two or more simpler figures. (11.4)
Volume of a Pyramid
V = ⅓Bh, B is the area of the base, h is the height of the pyramid. (11.5)
Volume of a Cone
V = ⅓Bh, B is the area of the base, h is the height of the pyramid.
V = ⅓πr²h, r is the radius, h is the height of the cone. (11.5)
Sphere
The set of all points in space that are a given distance, r (the radius), from a given point, C (the center). (11.6)
Great Circle
A circle in which the center is also the center of the sphere. (11.6)
Radius of a Sphere
A segment that has one endpoint at the center and the other endpoint on the sphere. (11.6)
Diameter of a Sphere
A segment passing through the center with endpoints on the sphere. (11.6)
Hemisphere
Half of a sphere. (11.6)
Surface Area of a Sphere
SA = 4πr², r is the radius. (11.6)
Volume of a Sphere
V = (4/3)πr³, r is the radius. (11.6)
Similar Solids
Solids that have the same shape, and all their corresponding dimensions are proportional. (11.7)
Similar Solid Ratios
If the scale factor of two similar solids is a:b, then the ratio of the their corresponding areas is: a²:b² and the ratio of their corresponding volumes is: a³:b³. (11.7)
Lateral Area
The sum of the areas of the lateral faces. (11.2)
Surface Area
The sum of the lateral area and the area of the two bases. (11.2)
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