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English6.1SpanishDrawing 3-Dimensional FiguresHow can you draw three-dimensional figures?SSTATESTANDARDSMA.7.G.2.1Dot paper can help you draw three-dimensional figures, or solids. Shading parallelsides the same color helps create a three-dimensional illusion.1Square Dot PaperIsometric Dot PaperFace-On ViewCorner ViewACTIVITY: Finding Surface Areas and VolumesWork with a partner.Draw the front, side, and top views of each stack of cubes. Then find thesurface area and volume. Each small cube has side lengths of 1 unit.a. Sample:topfrontsideVolume: 3 cubic unitsSurface Area: 14 square units250Chapter 6b.c.d.e.f.g.Surface Areas of Solids
EnglishSpanish2ACTIVITY: Drawing SolidsWork with a partner.a. Draw all the different solids you can make by joining four cubes. (Twohave been drawn.) Cubes must be joined on faces, not on edges only.Translations, reflections, and rotations do not count as different solids.Same solid reflectedb. Do all the solids have the same surface area? Do all the solids have the samevolume? Explain your reasoning.3. IN YOUR OWN WORDS How can you drawthree-dimensional figures? Draw and shadetwo prisms that have the same volume butdifferent surface areas.4. Maurits Escher (1898 –1972) was a popularartist who drew optical illusions.a. What is the illusion in Escher’s drawing?b. Why is the cartoon funny? What is theillusion in the cartoon? 2008 M.C. Escher’s “Ascending and Descending”Use what you learned about three-dimensional figures to completeExercises 7–9 on page 254.Section 6.1Drawing 3-Dimensional Figures251
English6.1SpanishLessonLesson TutorialsA three-dimensional figure, or solid, has length, width, and depth.A polyhedron is a three-dimensional figure whose faces are all polygons.Key Vocabularythree-dimensionalfigure, p. 252polyhedron, p. 252lateral face, p. 252PrismsA prism is a polyhedron that hastwo parallel, identical bases. Thelateral faces are parallelograms.PyramidsA pyramid is a polyhedron thathas one base. The lateral facesare triangles.BaseLateral faceBaseLateral faceBaseTriangular PrismRectangular PyramidThe shape of the base tells thename of the prism or the pyramid.CylindersA cylinder is a solid that has twoparallel, identical circular bases.ConesA cone is a solid that has onecircular base and one EXAMPLE1Drawing a PrismDraw a rectangular prism.252Chapter 6Step 1Step 2Step 3Draw identicalrectangular bases.Connect correspondingvertices.Change any hiddenlines to dashed lines.Surface Areas of Solids
EnglishSpanishEXAMPLE2Drawing a PyramidDraw a triangular pyramid.Step 1Step 2Step 3Draw a triangularbase and a point.Connect the vertices ofthe triangle to the point.Change any hiddenlines to dashed lines.Draw the solid.1. Square prismExercises 10 –15EXAMPLE32. Pentagonal pyramidDrawing Views of a SolidDraw the front, side, and top views of the paper cup.The front view isa triangle.The side view isa triangle.The top view isa circle.Draw the front, side, and top views of the solid.Exercises 16 –213.4.5.Section 6.1Drawing 3-Dimensional Figures253
EnglishSpanishExercises6.1Help with Homework1. VOCABULARY Compare and contrast prisms and cylinders.2. VOCABULARY Compare and contrast pyramids and cones.3. WRITING Give examples of prisms, pyramids, cylinders, and cones in real life.Identify the shape of the base. Then name the solid.4.5.6.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Draw the front, side, and top views of the stack of cubes. Then find the surface areaand volume.7.8.9.Draw the solid.12 10. Triangular prism13. Hexagonal pyramid11. Pentagonal prism12. Rectangular pyramid14. Cone15. CylinderDraw the front, side, and top views of the solid.2543 16.17.18.19.20.21.Chapter 6Surface Areas of Solids
EnglishSpanish22. PYRAMID ARENA The Pyramid of Caius Cestiusin Rome is in the shape of a square pyramid.Draw a sketch of the pyramid.23. RESEARCH Use the Internet to find a picture ofthe Washington Monument. Describe its shape.Draw a solid with the following front, side, and top views.24.25.frontsidetopfrontsidetop26. PROJECT Design and draw a house. Name the different solids that can beused to make a model of the house.27. REASONING Two of the three views of a solid are shown.a. What is the greatest number of unit cubes in the solid?b. What is the least number of unit cubes in the solid?topc. Draw the front views of both solids in parts (a) and (b).side28.Draw two different solids with five faces.a. Write the number of vertices and edges for each solid.b. Explain how knowing the numbers of edges and vertices helpsyou draw a three-dimensional figure.Find the area. SKILLS REVIEW HANDBOOK29.30.4m31.6 ft3 cm3 ft8 cm4 ft7m32. MULTIPLE CHOICE You borrow 200 and agree to repay 240 at the end of2 years. What is the simple interest rate per year?SECTION 4.4A 5% B 10% C 15% Section 6.1D 20% Drawing 3-Dimensional Figures255
Draw the solid. 1. Square prism 2. Pentagonal pyramid EXAMPLE 3 Drawing Views of a Solid Draw the front, side, and top views of the paper cup. The front view is The side view is The top view is a triangle. a triangle. a circle. Draw the front, side, and top views
