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Lesson 12-x, 13-y 3D Figures Review

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Objectives Review 3-D Figures Quiz on Friday Ch Test after SOLs

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Vocabulary None new

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Nets Triangular Prism Square Prism (Cube) Cylinder h r h C Nets – cut a 3d figure on its edges and lay it flat. It can be folded into the shape of the 3d figure with no overlap Surface Area – Sum of each area of the faces of the solid

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Spheres – Surface Area & Volume V = 4/3 * π * r 3 Sphere r SA = 4 π * r 2 Sphere – All points equal distant from a center point in 3-space Circles – Intersection between a plane and a sphere Great Circles – Intersections between a plane passing through the center of the sphere and the sphere. Great circles have the same center as the sphere. The shortest distance between two points on a sphere lie on the great circle containing those two points. Hemisphere – a congruent half of a sphere formed by a great circle. Surface areas of hemispheres are half of the SA of the sphere and the area of the great circle. Volumes of hemispheres are half of the volume of the sphere. V = 2/3 * π * r 3 SA = 3 π * r 2

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Cylinders – Surface Area & Volume Cylinder h r Volume (V) = B * h Base Area (B) = π * r 2 V = π * r 2 * h r – radius h – height Surface Area = Lateral Area + Base(s) Area h C Net LA = 2 π * r * h = circumference * h Bases Area = 2 * π * r 2 SA = LA + BA SA = 2 π * r * h + 2 π * r 2

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Prisms – Areas & Volumes Regular Triangular Prism Lateral Area (LA) – Sum of each area of the non-base(s) faces of the solid Surface Area (SA) – Sum of each area of (all) the faces of the solid Surface Area = Lateral Area + Base(s) Area h b b b b l LA = 3 * b * l = Perimeter * l Bases Area = 2* ½ * b * h SA = LA + BA SA = 3 * b * l + b * h base perimeter Rectangular Prism Volume (V) = B * h Base Area (B) = L * w V = L * w * h L w h LA = 2 * w * h + 2 * L * h Bases Area = 2 * L * w SA = LA + BA SA = 2(Lw + Lh + wh) Net

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Cones – Surface Area & Volume h r l Cone Cone – A solid with circular base and a vertex. l – slant height h – height Volume (V) = 1/3 * B * h Base Area (B) = π * r 2 V = 1/3 * π * r 2 * h Surface Area = Lateral Area + Base(s) Area LA = π * r * l Base Area = π * r 2 SA = LA + BA SA = π * r * l + π * r 2 l r Net

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Pyramids – Surface Area & Volume Volume (V) = 1/3 * B * h Base area (B) = area of the base example above V = 1/3 * s 2 * h Pyramid (Square) h B l l – slant heightSurface Area = Lateral Area + Base(s) Area LA = 4 * ½ s * l Bases Area = s * s = s 2 SA = LA + BA SA = 2 * s * l + s 2 In general: Pyramid LA = ½ P * l s s l ½ perimeter Net

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Summary & Homework Summary: –Nets fold up into 3 dimensional figures –Formulas are on formula sheet –Must identify needed variables –Lateral surface area (LA) is the area of the sides –Base surface area (B) is the area of the top/bottom –Surface area = Lateral Area + Base(s) Area –Common Error: b is a length and B is an area Homework: –study for Quiz

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