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Geometry > Chapter 11 > Flashcards

Chapter 11 Flashcards

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0
Q

Polyhedron

A

A polyhedron is a three dimensional figure whose surfaces are polygons (poly=many, hedron=side)

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1
Q

Euler’s Formula

A

The number of faces, vertices, and edges of a polyhedron are related by the formula F+V=E+2

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2
Q

Face

A

A face is each polygon on the polyhedron

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3
Q

Edge

A

An edge is a segment that is formed by the intersection of two faces

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4
Q

Vertex

A

A vertex is a point where the three or more edges meet

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5
Q

Cross section

A

A cross section is the intersection of a solid and a plane

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6
Q

Theorem 11-1: Lateral Surface Area of a Prism

A

The lateral area of a right prism is the product of the perimeter of the base and the height

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7
Q

Surface Area of a Right Prism

A

The surface area of a right prism is the sum of the lateral area and the area of the two bases

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8
Q

Prism and Bases

A

A prism is a polyhedron with exactly two congruent, parallel faces. These faces are called bases.

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9
Q

Lateral Faces

A

Lateral faces are the other faces

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10
Q

Altitude

A

An altitude is the perpendicular segment that joins the planes of the bases

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11
Q

Height

A

The height of the prism is the length of an altitude

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12
Q

Slant Height of a Regular Pyramid

A

The slant height of a regular pyramid is the length of the altitude of a lateral face of the pyramid

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13
Q

Surface Area of a Pyramid

A

The surface area of a pyramid is the area of its base added to the lateral area

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14
Q

Theorem 11-4: Lateral and Surface Areas of a Cone

A

The lateral area of a right cone is half the product of the circumference if the base and the slant height.

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15
Q

Surface Area of a Right Cone

A

The surface area of a right cone is the sum of the lateral area and the area of the base

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16
Q

Cone

A

A cone is a “pointed” like a pyramid, but it’s base is a circle

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17
Q

Right cone

A

In a right cone, the altitude is a perpendicular segment from the vertex to the center of the base

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18
Q

Slant Height of a Cone

A

The slant height of a cone is the distance from the vertex to a point on the edge of the base

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19
Q

Lateral Area

A

The lateral area is 1/2 the perimeter (circumference) of the base times the slant height

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20
Q

Surface Area

A

The surface area is the same as the pyramid, the lateral area plus the area of the base

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21
Q

Theorem 11-5: Cavalieri’s Principle

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A

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

22
Q

Theorem 11-6: Volume of a Prism

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A

The volume of a prism is the product of the area of a base and the height of the prism. V=Bh

23
Q

Volume

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A

Volume is the space that a figure occupies. Measured in cubic units

24
Composite Space Figure
A composite space figure is a three dimensional figure that is the combination of two or more simpler figures
25
Lateral Area
The lateral area of a prism is the sum of the areas of the lateral faces
26
Surface Area
The surface area is the sum of the lateral area and the area of the two bases
27
Right Prism
In a right prism the lateral faces are rectangles and lateral edge is an altitude
28
Oblique Prism
In an oblique prism some or all of the lateral faces are non-rectangular
29
Theorem 11-2: Lateral and Surface Areas of a Cynlinder
The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder
30
Surface Area of a Right Cylinder
The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases
31
Cylinder
A cylinder has two congruent parallel bases
32
Bases
The bases are circles
33
Lateral Area of a Cylinder
The lateral area of a cylinder is the area after you unroll it- it results in a rectangle
34
Right Cylinder
In a right cylinder, the segment joining the centers of the bases is not perpendicular to the planes containing the bases
35
Theorem 11-3: Lateral Area and Surface Area of a Regular Pyramid
The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height
36
Surface Area of a Regular Pyramid
The surface area of a regular pyramid is the sum of the lateral area and the area of the base
37
Pyramid
A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (lateral faces) are triangles that meet at a common vertex
38
Regular Pyramid
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles
39
Slant Height of a Regular Pyramid
The slant height of a regular pyramid is the length of the altitude of a lateral face of the pyramid
40
Lateral Area of a Pyramid
The lateral area of a pyramid is the sum of the areas of the congruent lateral faces
41
Surface Area of a Pyramid
The surface area of a pyramid is the tea of it base added to the lateral area
42
Surface Area of a Pyramid
The surface area of a pyramid is the area of its base added to the lateral area
43
Theorem 11-7: Volume of a Cylinder
The volume of a cylinder is the product of the area of the base and the height of the cylinder.
44
Theorem 11-8: Volume of a Pyramid
The volume of a pyramid is one third the product of the area of the base and the height of the pyramid V=1/3bh
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Theorem 11-9: Volume of a Cone
The volume of a cone is one third the product of the area of the base and the height of the cone V=1/3bh
46
Theorem 11-10: Surface Area of a Sphere
The surface area of a sphere is four times the product of pi and the square of the radius of the sphere
47
Theorem 11-11: Volume of a Sphere
The volume of a sphere is four thirds the product of pi and the cube of the radius of the sphere
48
Sphere
A sphere is the set of all points in space equidistant from a given point called the center
49
Radius
A radius is a segment that has one endpoint at the center and the other endpoint on the sphere
50
Diameter of a Sphere
A diameter of a sphere is a segment passing through the center with endpoints on the sphere
51
Great Circle
A great circle is the intersection of a sphere and the plane containing the center of the sphere. A great circle divided a sphere into two hemispheres
52
Theorem 11-12: Areas and Volumes of Similar Solids
If the similarity ratio of two solids is a:b, then 1. The ratio of theirs corresponding areas is a2:b2 2. The ratio of their volumes is a3:b3
53
Similar Solids
Similar solids have the same shape and all their corresponding dimensions are proportional

Geometry (5 decks)

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