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Chapter 12

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Section 12-1

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Also called solids Enclose part of space

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Solids with flat surfaces that are polygons

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

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

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

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

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

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Section 12-2

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

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

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

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

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

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Section 12-3

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The measurement of the space contained within a solid figure

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

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

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Section 12-4

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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

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A right pyramid whose base is a regular polygon

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

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

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

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

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Surface Area of a Cone S = rl + r 2

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Section 12-5

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

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

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Section 12-6

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

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A line that intersects the sphere at exactly one point

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

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Volume of a Sphere V = 4/3 r 3

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Section 12-7

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

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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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11.3 Surface Areas of Pyramids and Cones A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces)

11.3 Surface Areas of Pyramids and Cones A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces)

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