 # Chapter 12. Section 12-1  Also called solids  Enclose part of space.

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Chapter 12

Section 12-1

 Also called solids  Enclose part of space

 Solids with flat surfaces that are polygons

 Faces – 2-dimensional surfaces formed by polygons  Edge – where 2 faces intersect  Vertex – the point where 3 or more edges intersect

 Two parallel faces called bases that are congruent polygons  Other faces are called lateral faces  Lateral faces intersect in lateral edges

 All faces except the base intersect at the vertex  The triangular faces that meet at the vertex are called lateral faces

 The two bases are congruent, parallel circles  The lateral surface is curved

 The base is a circle  The lateral surface is curved  The point is called the vertex

Section 12-2

 Lateral Area - The sum of the areas of its lateral faces  Surface Area – The sum of the areas of all its surfaces

 Lateral Area of a Prism  L = Ph  P= perimeter of the base  h= height of the prism

 Surface Area of a Prism  S = Ph + 2b  B = area of the base

 Lateral Area of a Cylinder  L = 2  rh  r = radius of the base  h= height of the cylinder

 Surface Area of a Cylinder  S = 2  rh + 2  r 2

Section 12-3

 The measurement of the space contained within a solid figure

 Volume of a Prism  V = Bh  B = area of the base  h = height of the prism

 Volume of a Cylinder  V =  r 2 h  r = radius of the base  h = height of the cylinder

Section 12-4

 The segment from the vertex perpendicular to the base  In a right pyramid or cone, the altitude is perpendicular to the center  In an oblique pyramid or cone, the altitude is perpendicular at another point

 A right pyramid whose base is a regular polygon

 The height of each lateral face of a pyramid  Represented by l

 Lateral Area of a Regular Pyramid  L = ½ Pl  P = perimeter of the base  l = slant height

 Surface Area of a Regular Pyramid  S = ½ Pl + B  B = area of the base

 Lateral Area of a Cone  L =  rl  r = radius of the base  l = slant height of the cone

 Surface Area of a Cone  S =  rl +  r 2

Section 12-5

 Volume of a Pyramid  V = 1/3Bh  B = area of the base  h = height of the pyramid

 Volume of a Cone  V = 1/3  r 2 h  r = radius of the base  h = height of the cone

Section 12-6

 A sphere is a set of all points that are a given distance from a given point called the center.

 A line that intersects the sphere at exactly one point

 Surface Area of a Sphere  S = 4  r 2  r = radius of the sphere

 Volume of a Sphere  V = 4/3  r 3

Section 12-7

 For similar solids, the corresponding lengths are proportional, and the corresponding faces are similar.

 If two solids are similar with a scale factor of a:b, then the surface areas have a ratio of a 2 :b 2 and the volumes have a ratio of a 3 :b 3

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