Slide 1 / 219 Slide 2 / 219 New Jersey Center for Teaching and Learning Surface Area Progressive Mathematics Initiative & This material is made freely available at www.njctl.org Volume and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course March 7, 2012 materials to parents, students and others. www.njctl.org Click to go to website: www.njctl.org Slide 3 / 219 Slide 4 / 219 Table of Contents 1. Drawing 3-D Figures 7. Surface Area of a Cylinder 2. Surface v. Solid 8. Surface Area of a Pyramid 3. Right v. Oblique 9. Surface Area of a Cone Understanding 3-Dimensional Drawings 4. Nets 10. Spheres 5. Views 11. Surface Area of a Sphere 6. Surface Area of a Prism Return to Table of Contents Click on the topic to go to that section Slide 5 / 219 Slide 6 / 219 2-dimensional drawings use only the x and y axes X Y Y Length width Y width X X Length X w i d Y t h Length X Y
Slide 7 / 219 Slide 8 / 219 3-dimensional drawings include the x, y and z-axis. Z The z-axis is the third dimension. Z The third dimension is the height of the figure height height height height X X X X Y Y Y Y Slide 9 / 219 Slide 10 / 219 Y Z Y Z r x X height height height X X Y Y X X Y Y Slide 11 / 219 Slide 12 / 219 To give a figure more of a 3-dimensional, lines that are not visible from the angle the figure is being viewed are drawn as dashed line segments. These are called The 3-Dimensional Figures discussed in hidden lines. this unit are: Z Prisms Pyramids Cylinders Cones height Spheres height X Y
Slide 13 / 219 Slide 14 / 219 Prisms have 2 congruent polygon bases. The sides of The polygons that make up the surface of the figure are a base are called base edges. called faces. The bases are a type of face and are The segments connecting corresponding vertices are parallel and congruent to each other. The lateral edges lateral edges. are the sides of the lateral faces. A A B B C C X X Y Y In this diagram: In this diagram: There are 2 bases: ABC & XYZ. There are 2 bases: ABC & XYZ. Z Z There are 6 base edges: AB, BC, AC, XY, YZ, & XZ. There are 6 base edges: AB, BC, AC, XY, YZ, & XZ. There are 3 lateral edges: AX, BY, & CZ. There are 3 lateral edges: AX, BY, & CZ. This prism has a total of 9 edges. This prism has a total of 9 edges. Slide 15 / 219 Slide 16 / 219 Choose all of the base edges. Choose all of the lateral edges. 1 2 A A B B C C A A B B D D E E F F C C N N P P D D M Q M Q E E S R S R F F G G H H I I Slide 17 / 219 Slide 18 / 219 Choose all of the edges. 3 4 Chooses all of the bases. AFSM A A B C A B C A D FERS B B D E F E F C C EDQR N P N P D ABCDEF D M Q M Q S R CDQP E R E S BCPN F F MNPQRS G G H H ABNM I
Slide 19 / 219 Slide 20 / 219 5 Chooses all of the lateral faces. 6 Chooses all of the faces. AFSM AFSM A A B C B C A A D D FERS FERS B B E E F F EDQR EDQR C C N N P P D ABCDEF D ABCDEF M Q M Q S R S R CDQP CDQP E E BCPN BCPN F F MNPQRS MNPQRS G G ABNM ABNM H H Slide 21 / 219 Slide 22 / 219 A pyramid has 1 base and the lateral edges go to a A pyramid is faces that are polygons. 1 base and single point. This point is called the vertex. triangles that are the lateral faces. A A This pyramid has: This pyramid has: 6 lateral edges, 6 lateral faces, 6 base edges, N 1 base, N P P 12 edges (total) 7 faces (total) M Q M Q S R S R Slide 23 / 219 Slide 24 / 219 7 Choose all of the base edges. 8 Choose all of the base edges. A V A V B B C C N N K K M M D D E E L L F F
Slide 25 / 219 Slide 26 / 219 9 How many edges does the pyramid have? 10 Choose all of the lateral faces. V V KNV A NMV B N KLMN C K N M K M D VML L KLV L E Slide 27 / 219 Slide 28 / 219 11 Choose all of the bases. 12 How many faces does the pyramid have? V A KNV V NMV B N KLMN C K M N K VML M D L KLV E L Slide 29 / 219 Slide 30 / 219 A cone, like a pyramid, has one base which is a circle. . N is the base of the cone. V V is the vertex of the cone.
Slide 31 / 219 Slide 32 / 219 13 Which shape has 2 bases? A sphere is a 3-dimensional circle in that every point on the sphere is the same distance from Prism A the center. Pyramid B Cylinder C D Cone Sphere E . C Slide 33 / 219 Slide 34 / 219 14 Which shape has a vertex? 15 Which shape has more base edges than lateral edges? A Prism Prism A Pyramid B B Pyramid Cylinder C Cylinder C Cone D Cone D Sphere E Sphere E Slide 35 / 219 Slide 36 / 219 16 Which shape has no vertices? Prism A Pyramid B Cylinder C Surface v. Solid D Cone Sphere E Return to Table of Contents
Slide 37 / 219 Slide 38 / 219 17 Is the following object a solid or a surface? Surfaces and Solids are 3-dimensional figures. A Brick Solid A A solid is a A surface is the shell of a figure. filled figure. Surface B In drawings, a solid is shaded so you cannot see through it. Slide 39 / 219 Slide 40 / 219 18 Is the following object a solid or a surface? 19 Is the following object a solid or a surface? An empty shoe box A new can of soda A Solid A Solid Surface Surface B B Slide 41 / 219 Slide 42 / 219 A cross-section is the locus of points of the 20 Is the following object a solid or a surface? intersection of a plane and a space figure. An ice cream cone Solid A Surface B
Slide 43 / 219 Slide 44 / 219 Think about as if the plane were a knife and you were Cross-sections of a surface are a 2-dimensional figure. cutting the shape, what would the cut look like? Cross-sections of a solid are a 2-dimensional figure and its interior. (The top can be removed to see the cross section.) Slide 45 / 219 Slide 46 / 219 21 What is the locus of points (cross-section) of a cube 22 What is the locus of points of a cube and a plane that and a plane perpendicular to the base and parallel to contains the diagonal of the base and is perpendicular the non-intersecting sides? to the base? A square square A B rectangle B rectangle trapezoid trapezoid C C hexagon hexagon D D rhombus rhombus E E parallelogram parallelogram F F G triangle G triangle circle circle H H Slide 47 / 219 Slide 48 / 219 23 What is the locus of points of a cube and a plane that 24 What is the locus of points of a cube and a plane that contains the diagonal of the base but does not intersects all of the faces? intersect the opposite base? square square A A rectangle rectangle B B trapezoid trapezoid C C D hexagon D hexagon rhombus rhombus E E parallelogram parallelogram F F triangle triangle G G circle circle H H
Slide 49 / 219 Slide 50 / 219 25 Choose all of the following that have cross-sections that consist of a 2-dimensional shape and its interior. a brick A B a balloon an empty soda can C Right v. Oblique a stick of butter D a wrapping paper tube E a baseball F Return to Table of Contents G a straw a book H Slide 51 / 219 Slide 52 / 219 Right Triangular Prism Oblique Triangular Prism Oblique lines- two lines that intersect and are not perpendicular. Slide 53 / 219 Slide 54 / 219 Right Cylinder Oblique Cylinder Right Hexagonal Pyramid Oblique Hexagonal Pyramid A right pyramid with a regular polygon for the base is called a regular pyramid. So this surface How can a right prism or cylinder be could also be called a regular distinguished from an oblique figure? hexagonal pyramid.
Slide 55 / 219 Slide 56 / 219 Right Cone Oblique Cone Right Triangular Prism Oblique Triangular Prism What shape is each What shape is each lateral face? lateral face? How can a right pyramid or cone be distinguished from an oblique figure? Slide 57 / 219 Slide 58 / 219 Naming a Figure Pyramid Right Shape Solid or of or or Oblique Base Prism Surface Since cones and cylinders always circles as bases: Right Cylinder Solid or or or Oblique Surface Cone Triangular Cylinder Right A sphere is neither right or oblique: Solid Pentagonal Cone Square Pyramid Oblique Surface Hexagonal Solid Spherical or Rectangle Prism Surface Slide 59 / 219 Slide 60 / 219 Triangular Cylinder Triangular Cylinder Right Right Solid Solid Pentagonal Pentagonal Cone Cone Square Square Pyramid Pyramid Oblique Oblique Surface Surface Hexagonal Hexagonal Prism Prism Rectangle Rectangle
Slide 61 / 219 Slide 62 / 219 Triangular Cylinder Triangular Cylinder Right Right Solid Solid Pentagonal Pentagonal Cone Cone Square Square Pyramid Pyramid Oblique Surface Oblique Surface Hexagonal Hexagonal Prism Prism Rectangle Rectangle Slide 63 / 219 Slide 64 / 219 Net A Net is a 2-dimensional shape that folds into a 3- dimensional figure. The Net shows all of the faces of the surface. Nets Return to Table of Contents Slide 65 / 219 Slide 66 / 219 Net Net Shown is the net of a right rectangular prism. 4 6 12 12 The net shown is a right triangular prism. The lateral faces are 4 6 6 4 rectangles. The bases are on opposite sides of the rectangles, although they do not need to be on the same rectangle. 4 6
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