3 A polyhedron is a solid bounded by polygons A polyhedron is a solid bounded by polygons. Sides are faces, edges are line segments connecting faces, and vertices are points where the edges meet. The plural of polyhedron is polyhedra or polyhedrons.A polyhedron is regular if all the faces are congruent regular polygons.A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely on the polyhedron (like with polygons)There are 5 regular polyhedra, called Platonic solids (they’re just friends). They are a (look at page 721):tetrahedron (4 triangular faces) a cube (6 square faces) octahedron (8 triangular faces) dodecahedron (12 pentagonal faces) icosahedron (20 triangular faces)
5 Is it a polyhedron. If so, count the faces, edges, and vertices Is it a polyhedron? If so, count the faces, edges, and vertices. Also say whether or not it is convex.No
6 Euler’s Theorem:(Like FAVE two, or cube method)Edges = Sides/2Find vertices of polyhedra made up of 8 trapezoids, 2 squares, 4 rectangles.Find vertices of polyhedra made up of 2 hexagons, 6 squares.
7 The intersection of a plane crossing a solid is called a cross section The intersection of a plane crossing a solid is called a cross section. Sometimes you see it in bio, when they show you the inside of a tree, the circle you get when you slice a tree is called the cross section of a tree.
9 TermsP Perimeter of one baseB Area of baseb base (side)h Height (relating to altitude)l Slant HeightTA Total Area (Also SA for surface Area)LA Lateral AreaV Volume
10 Prism Net View A prism has two parallel bases. Altitude is segment perpendicular to the parallel planes, also referred to as “Height”.Lateral faces are faces that are not the bases. The parallel segments joining them are lateral edges.PrismNet View
11 If the lateral faces are rectangles, it is called a RIGHT PRISM If the lateral faces are rectangles, it is called a RIGHT PRISM. If they are not, they are called an OBLIQUE PRISM.Altitude.Lateral edge not an altitude.RIGHT PRISMOBLIQUE PRISM.
12 Lateral Area of a right prism is the sum of area of all the LATERAL faces. = bh + bh + bh + bh= (b + b + b + b)hLA= PhTotal Area is the sum of ALL the faces.TA= 2B + Ph
52 Hexagon is regular, the box is not Hexagon is regular, the box is not. Hexagon radius 4 units, height is 6 units Finding the volume of box with hexagonal hole drilled in it.Find volume. Units in meters.812
55 A sphere with center O and radius r is the set of all points in SPACE with distance r from point O. Great Circle: A plane that contains the center of a circle.Hemisphere: Half a sphere.Chord: Segment whose endpoints are on the sphereDiameter: Segment through center of the sphere
61 Find the total area and volume of a cube with side lengths: Area Volume12510
62 Two shapes are similar if all the the sides have the same scale factor. If the scale factor of two similar solid is a:b, thenThe ratio of the corresponding perimeters is a:bThe ratio of the base areas, lateral areas, and total areas is a2:b2The ratio of the volumes is a3:b3
63 Surface area of A Surface Area of B Volume of A Volume of B Given the measure of the solids, state whether or not they are similar, and if so, what the scale factor is.Surface area of ASurface Area of BVolume of AVolume of BScale Factor10014412521649641827
64 Two similar cylinders have a scale factor of 2:3 Two similar cylinders have a scale factor of 2:3. If the volume of the smaller cylinder is 16π units3 and the surface area is 16π units2, then what is the surface area and volume of the bigger cylinder?
65 Two similar hexagonal prisms have a scale factor of 3:4 Two similar hexagonal prisms have a scale factor of 3:4. The larger hexagon has side length 4 in and height 9 in. Find the surface area and volume of the smaller prism using ratios.