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

Objectives Review 3-D Figures Quiz on Friday Ch 11-13 Test after SOLs

Vocabulary None new

Nets Cylinder Triangular Prism 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 h h r C Square Prism (Cube) Surface Area – Sum of each area of the faces of the solid

Spheres – Surface Area & Volume 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. r V = 4/3 * π * r3 SA = 4π * r2 Sphere – All points equal distant from a center point in 3-space V = 2/3 * π * r3 SA = 3π * r2

Cylinders – Surface Area & Volume r – radius h – height Net h h C r Volume (V) = B * h Base Area (B) = π * r2 V = π * r2 * h Surface Area = Lateral Area + Base(s) Area LA = 2π * r * h = circumference * h Bases Area = 2 * π * r2 SA = LA + BA SA = 2π * r * h + 2π * r2

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

Cones – Surface Area & Volume Net l l – slant height h – height h r Surface Area = Lateral Area + Base(s) Area Cone – A solid with circular base and a vertex. LA = π * r * l Base Area = π * r2 SA = LA + BA SA = π * r * l + π * r2 Volume (V) = 1/3 * B * h Base Area (B) = π * r2 V = 1/3 * π * r2 * h

Pyramids – Surface Area & Volume Pyramid (Square) l h B l s Net s Surface Area = Lateral Area + Base(s) Area l – slant height ½ perimeter Volume (V) = 1/3 * B * h Base area (B) = area of the base example above V = 1/3 * s2 * h LA = 4 * ½ s * l Bases Area = s * s = s2 SA = LA + BA SA = 2 * s * l + s2 In general: Pyramid LA = ½ P * l

Summary & Homework Summary: Homework: 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