Views Of Three-Dimensional Objects - Ms. Rae
Views of Three-DimensionalObjectsFocus on After this lesson,you will be able to.! draw and labeltop, front, andside views of3-D objects! build 3-Dobjects whengiven top, front,and side viewsSable and Josh are trying to build exactly the same three-dimensional 20 unit blocks masking tape isometric dot paperA iZgVXnA c To describe athree-dimensional(3-D) object, count itsfaces, edges, andvertices.Face:flat orcurvedsurfaceEdge: linesegmentwhere twofaces meetVertex: pointwhere three ormore edges meet164MHR Chapter 5(3-D) object. They each have the same number of blocks, but theycannot see each other’s object.Using a common vocabulary can help Sable and Josh build thesame object.How can you describe and build three-dimensional objects?1.Work with a partner. Create a 3-D object using ten unit blocks.Make sure your partner cannot see your object.2.Describe your completed object to your partner, and have yourpartner try to build the same object. What key words did youuse that were helpful?3.Decide which faces will be the front and top of your object. Thendetermine which faces are the bottom, left side, right side, and back.You may wish to label the faces with tape. Then, describe yourobject to your partner again. Was it easier to describe this time?
4.Using isometric dot paper, draw what your object looks like.Reflect on Your FindingsDo you need to know all the views to construct an object?If not, which ones would you use and why?b) Explain why you might need to have only one side view,if the top and front views are also given.c) Are any other views unnecessary? Are they needed toconstruct the same object?5. a)Using isometric dot paper makesit easier to draw 3-D shapes.Follow the steps to draw arectangular solid.1324Each view shows twodimensions. Whencombined, these viewscreate a 3-D diagram.Example 1: Draw and Label Top, Front, and Side ViewsUsing blank paper, draw the top, front, and side views of these items.Label each view.a)Tissue boxb)Compact disk caseSolutiona)topb)topfrontfrontside(end of the box)side5.1 Views of Three-Dimensional Objects MHR165
Using blank paper, draw the top, front, andside views of this object.Example 2: Sketch a Three-Dimensional Object When Given ViewsArchitects use topviews to drawblueprints forbuildings.These views were drawn for an object made of ten blocks.Sketch what the object looks like.topsidefrontSolutionUse isometric dot paperto sketch the object.An object is created using eightblocks. It has the following top,front, and side views. Sketch whatthe object looks like on isometricdot paper.166MHR Chapter 5topfrontside
Example 3: Predict and Draw the Top, Front, and Side ViewsAfter a RotationThe diagrams show the top, front, and side views of the computer tower.topfrontsideYou want to rotate the computer tower 90º clockwise on its base to fitinto your new desk. Predict which view you believe will become thefront view after the rotation. Then, draw the top, front, and side viewsafter rotating the tower.This diagram showsa 90 clockwiserotation.90 SolutionThe original side view will become the new front view after the rotation.topfrontsideYou can use a Drawprogram to create3-D objects.Stand your MathLinks 8 student resource on your desk. Predict whatthe top, front, and side views will look like if you rotate it 90ºclockwise about its spine. Then, draw the top, front, and side viewsafter rotating the book.5.1 Views of Three-Dimensional Objects MHR167
A minimum of three views are needed to describe a 3-D object. Using the top, front, and side views, you can build or draw a3-D object.topsidefront1.Raina insists that you need to tell her all six views so she candraw your object. Is she correct? Explain why or why not.2.Are these views correct? Justify your answer.fronttopsidec)For help with #3 and #4, refer to Example 1 onpages 165–166.3.Sketch and label the top, front, andside views.a)b)4.PhotoAlbumChoose the correct top, front, and sideview for this object and label each one.A168MHR Chapter 5EBFCGD
For help with #5, refer to Example 2 on page 166.5.Draw each 3-D object using theviews below.a)b)toptopfrontfront8.Choose two 3-D objects from yourclassroom. Sketch the top, front, andside views for each one.9.Sketch the front, top, and right sideviews for these solids.sidesidea)For help with #6 and #7, refer to Example 3 onpage 167.6.frontfrontfrontc)A television set has the following views.topb)sidefrontIf you turn the television 90 counterclockwise, how would the threeviews change? Sketch and label eachnew view.7.Choose which objecthas a front view like thisafter a rotation of90º clockwise onto its side.a)b)set of booksCD rack10.Describe two objects that meet thisrequirement: When you rotate an object 90 ,the top, front, and side views are the same asthe top, front, and side views of the objectbefore it was rotated.11.An injured bumblebee sits at a vertex of acube with edge length 1 m. The bee movesalong the edges of the cube and comesback to the original vertex without visitingany other vertex twice.a) Draw diagrams to show thebumblebee’s trip around the cube.b) What is the length, in metres, of thelongest trip?MATH LINKChoose one of the essential buildings that you discussed for your new communityon page 163. Draw and label a front, side, and top view.5.1 Views of Three-Dimensional Objects MHR169
Nets of Three-DimensionalObjectsFocus on After this lesson, youwill be able to.! determine thecorrect nets for3-D objects! build 3-D objectsfrom nets! draw nets for3-D objectsrectangular prism a prism whose basesare congruent rectanglesShipping containers help distribute materials all over the world. Itemscan be shipped by boat, train, or transport truck to any destinationusing these containers. Shipping containers are right rectangular prisms .Why do you think this shape is used? grid paperscissorsclear taperectangular prisms(blocks of wood,cardboard boxes,unit blocks)How do you know if a net can build a right rectangular prism?Here are a variety of possible netsfor a right rectangular prism.net a two-dimensionalshape that, whenfolded, encloses a3-D objectnet170cubeMHR Chapter 5rectangular prismLiteracyLinkA right prism hassides that areperpendicular to thebases of the prism.1.Draw each net on grid paper.
2.Predict which nets will form a right rectangular prism.3.Cut each net out along the outside edges and fold along the insideedges, taping the cut edges to try to form a right rectangular prism.4.Do all the nets create right rectangular prisms?5.Place a right rectangular prism (such as a small cardboard box)on a piece of blank paper. “Roll” the prism onto its faces, traceeach face, and try to draw another correct net. Your net shouldbe different from the examples you have already made.Reflect on Your FindingsCompare the net you drew with those of three of yourclassmates. What is the same and different about your nets?b) Is there more than one way to draw a net for a 3-D object?Explain your answer.6. a)Example 1: Draw a Net for a Three-Dimensional ObjectA company asks you to create an umbrella standfor large beach umbrellas. Draw the net for theumbrella stand.SolutionVisualize what the umbrella stand would look like if you could cut itopen and flatten it. The net has one circle and a rectangle. When therectangle is curved around the circle, the net will form a cylinder withan open top. The width of the rectangle is equal to the circumferenceof the circle.Draw a net for an unopened soup can.5.2 Nets of Three-Dimensional Objects MHR171
Example 2: Build a Three-Dimensional Object From a Given NetBefore going to leadership camp, your group needs to put a tenttogether. Can this net be folded to form the shape of a tent?StrategiesModel Ittriangular prism a prism with twotriangular baseseach the same sizeand shapeSolutionTrace the net onto paper. Cut along the outside edges and foldalong the inside edges. Tape the cut edges together to try to builda right triangular prism .The net can be folded to form the shape of a tent.Build a 3-D object using this net. What objectdoes it make?172MHR Chapter 5
A net is a two-dimensional shape that, when folded,encloses a three-dimensional object.netcube The same 3-D object can be created by foldingdifferent nets. You can draw a net for an object by visualizing what it wouldlook like if you cut along the edges and flattened it out.1.Both of these nets have six faces, like a cube. Will both netsform a cube? Justify your answer.Net A2.Net BPatricia is playing the lead role in the school musical this year. Shemissed Math class while she was performing. She cannot figure outif a net will build the correct 3-D object, and asks you for help afterschool. Show how you would help her figure out this problem.For help with #3 to #5, refer to Example 1 on page 171.3.Sketch a net for each object.a)b)hockey puckc)chocolate barjewellery box5.2 Nets of Three-Dimensional Objects MHR173
4.Draw the net for each object. Label themeasurements on the net.a)7.Match each solid with its net. Copy thenets, then try to create the 3-D objects.d 30 mmrectangular prismA ream describes aquantity ofapproximately 500sheets of paper.78 mmcylinderb)triangular prismA28 cmPaper500 SheetsB5 cm21.5 cm5.Draw a net on grid paper for a rectangularprism with the following measurements:length is six units, width is four units, andheight is two units.CFor help with #6 and #7, refer to Example 2 onpage 172.6. a)DDraw the net on grid paper, as shown.Cut along the outside edges of the netand fold to form a 3-D object.Eb)1748.A box of pens measures 15.5 cm by 7 cmby 2.5 cm. Draw a net for the box on apiece of centimetre grid paper. Then, cutit out and fold it to form the box.9.You are designing a new mailbox. Drawa net of your creation. Include allmeasurements.What is this object called?MHR Chapter 5
10.Simon designed two nets.12.What colour is on the opposite side ofeach of these faces?a) purpleb) bluec) redEnlarge both nets on grid paper, andbuild the 3-D objects they form.b) What object does each net form?a)13.11.Hannah and Dakota design a spellingboard game. They use letter tiles to createwords. Tiles may be stacked (limit of four)on top of letters already used for a wordon the board to form a new word.a) Draw a 3-D picture of what thesestacked tiles might look like.b) Draw a top view that illustrates thestacked tiles for people reading theinstructions.The six sides of a cube are each adifferent colour. Four of the viewsare shown below.How many possible nets can create a cube?Sketch all of them. The first one is donefor you.MATH LINKWhen buildings are designed, it isimportant to consider engineeringprinciples, maximum andminimum height requirements,and budget.a) Create a 3-D sketch of twobuildings for your miniaturecommunity, one that is a prismand one that is a cylinder.b) Draw a net of each building,including all possiblemeasurements needed tobuild your miniature.5.2 Nets of Three-Dimensional Objects MHR175
Surface Area of a PrismFocus on After this lesson,you will be able to.! link area tosurface area! find the surfacearea of a rightprismMost products come in some sort of packaging. You can helpconserve energy and natural resources by purchasing products that are made using recycled material use recycled material for packaging do not use any packagingWhat other ways could you reduce packaging?How can you determine the surface area of a package? empty cardboard box(cereal box, granolabox, snack box, etc.) scissors ruler scrap paper1.Choose an empty cardboard box. Cut along edges of the box so itunfolds to form a net.Do you need toinclude the materialused in theoverlapping flaps?Why or why not?2.Suppose you want to design an advertisement to place on the outsideof your box. How can you determine the surface area you have towork with?Reflect on Your FindingsShare your method with several of your classmates. Discuss anysimilarities or differences between the methods.b) Which method do you prefer to use? Justify your response.3. a)176MHR Chapter 5
Example 1: Calculate the Surface Area of a Right Rectangular Prisma)Draw the net of this right rectangular prism.6 cm10 cmb)4 cmWhat is the surface area of the prism?surface area the number of squareunits needed to covera 3-D object the sum of the areas ofall the faces of anobjectSolutiona)10 cm4 cm6 cmb)The right rectangular prism has faces that are three different sizes.front or back4 cm4 cm6 cm10 cmendstop or bottom6 cm10 cmA l wA 10 6A 60A l wA 10 4A 40A l wA 6 4A 24The area of the frontor back is 60 cm2.The area of the topor bottom is 40 cm2.The area of eachend is 24 cm2.Area is measured insquare units.For example, squarecentimetres, squaremetres, etc.The surface area is the sum of the areas of all the faces.The front and backhave the same area:A 60 2A 120The top and bottomhave the same area:A 40 2A 80The two ends havethe same area:A 24 2A 48StrategiesHow else could youcalculate the surfacearea?Surface area (area of front and back) (area of top and bottom) (area of ends)You could add the areas you calculated 120 80 48first. 60 40 24 124 248The surface area of the right rectangular prismis 248 cm2.Each area is the same as the area of one otherface, so you could then multiply the total bytwo. 124 2 2485.3 Surface Area of a Prism MHR177
What is the surface area of this rightrectangular prism?16 cm8 cm3 cmExample 2: Calculate the Surface Area of a Right TriangularPrismDraw the net of this righttriangular prism.b) What is the surface area?a)2.6 m9m3mSolutiona)9mStrategiesDraw a Diagram3m2.6 mStrategiesWhat other strategiescould you use?b)The bases of the prism are equilateral triangles.The sides of the prism are rectangles.rectangletriangle2.6 m3mLiteracyLinkAn equilateral trianglehas three equal sidesand three equalangles. Equal sidesare shown ondiagrams by placingtick marks on them.178MHR Chapter 59mA l wA 9 3A 27The area of onerectangle is 27 m2.3mA (b h) 2A (3 2.6) 2A 7.8 2A 3.9The area of onetriangle is 3.9 m2.
This right triangular prism has five faces.There are three rectangles of the same size and two trianglesof the same size.Surface area (3 area of rectangle) (2 area of triangle) (3 27) (2 3.9) 81 7.8 88.8The surface area of the right triangular prism is 88.8 m2.Find the surface area of thistriangular prism.9.9 cm7 cm2 cm7 cm Surface area is the sum of the areas of all the faces of a 3-D object.A1A6A2A5A3A4Surface Area A1 A2 A3 A4 A5 A6,where A1 represents the area of rectangle 1, A2represents the area of rectangle 2, etc.1.Write a set of guidelines that you could use to find the surface areaof a prism. Share your guidelines with a classmate.2.A right rectangular prism has six faces. Why might you have tofind the area of only three of the faces to be able to find the surfacearea? Use pictures and words to explain your thinking.5.3 Surface Area of a Prism MHR179
7.For help with #3 and #4, refer to Example 1 onpage 177.3.4.Find the surfacearea of this rightrectangular prism tothe nearest tenth of asquare centimetre.Find the surface areaof this CD case.front13.5 cm5 cm8.3 cm9.1 cm180MHR Chapter 5Paco builds a glass greenhouse.14 cm1 cm1.1 m2.4 m1.8 m0.6 mHow many glass faces does thegreenhouse have?b) How much glass does Paco needto buy?a)0.7 mCheese is sometimes packaged in atriangular box. How much cardboardwould you need to cover this piece ofcheese if you do not include overlapping?Calculate your answer to the nearest tenthof a square centimetre.6.4 cm215 mm220 mm18.5 cmCalculate thesurface area of2.7 mthis ramp in the1.4 mshape of a righttriangular prism.2.3 mGive your answerto the nearest tenth of a square metre.4.5 cmside2For help with #5 to #7, refer to Example 2 onpages 178–179.6.top12 mm12.3 cm5.Given the area of each face of a rightrectangular prism, what is the surface area?The tick marks onthe two sides ofthe triangleindicate that thesesides are equal.9.What is the minimum amount of materialneeded to make the cover of this textbookif there is no overlap? Give your answer tothe nearest square millimetre.10.Jay wants to make a bike ramp. He drawsthe following sketch. What is the surfacearea of the ramp?0.9 m2.2 m2m1.6 m
11.Dallas wants to paint three cubes. Thecubes measure 1 m 1 m 1 m,2 m 2 m 2 m, and 3 m 3 m 3 m,respectively. What total surface area willDallas paint if he decides not to paint thebottoms of the three cubes?14.Ethan is hosting games night this weekend.He bought ten packages of playing cards.Each package measures 9 cm 6.5 cm 1.7 cm. He wants to build a container tohold all ten packages of cards.a) What are the minimum insidedimensions of the container?b) Is there more than one kind ofcontainer that would work? Drawdiagrams to help explain your answer.12.Tadika has a gift to wrap. Both of thesecontainers will hold her gift. Whichcontainer would allow her to use theleast amount of wrapping paper? Explainyour choice.15. a)If the edge length of a cube is doubled,find the ratio of the old surface area tothe new surface area.b) What happens if the edge length ofa cube is tripled? Is there a pattern?7 cm16.30 cm5 cm10 cm13.10 cm5 cmA square cake pan measures 30 cm oneach side and is 5 cm deep. Cody wantsto coat the inside of the pan with nonstick oil. If a single can of non-stick oilcovers an area of 400 000 cm2, howmany pans can be coated with a singlecan?Shelby wantsto paint thewalls andceiling of arectangularroom.Type of Paint2.6 m6.8 m4.8 mSize of Paint CanCostWall paint4L1L 24.95 7.99Ceiling paint4L 32.95One litre of paint covers 9.5 m2.a) What is the least amount of paint Shelbycan buy to paint the room (subtract 5 m2for the door and windows)?b) How much will the paint cost,including the amount of tax chargedin your region?MATH LINKFor the prism-shaped building you created in the Math Link on page 175, how muchmaterial do you need to cover the exterior walls and the roof of the building?5.3 Surface Area of a Prism MHR181
Surface Area of a CylinderFocus on After this lesson,you will be able to.! find the surfacearea of a cylinderGlow sticks work because of a chemical reaction. There are twosolutions in separate compartments inside the stick. Once you bend thestick, the two solutions mix. This mixture creates a new solution thatgives off light. The colour of the glow stick depends on the dye in themixture. How might you determine how much plastic would be neededto make a glow stick to fit around your wrist?cylinder a three-dimensionalobject with twoparallel and congruentcircular basesHow do you find the surface area of a right cylinder ?Work with a partner.Draw the net of a glow stick. Usethe actual dimensions from thediagram shown.b) Describe each face of your net.1. a)2.cylinder182MHR Chapter 5d 0.5 cm21 cmHow can you use what you know about circles to help you find thesurface area of the glow stick?
3.4.What is the surface area of the glow stick, to the nearest hundredthof a square centimetre? Include the units in your final answer.Share your strategies with another group.Reflect on Your Findings5.Pop cans arecylinders. The world’slargest Coke can islocated in Portage laPrairie, Manitoba.Would your method work for any right cylinder? Explainyour reasoning.Example 1: Determine the Surface Area of a Right CylinderEstimate the surface area of the can.b) What is the surface area of the can?Express your answer to the nearesthundredth of a square centimetre?a)11 cm7.5 cmSolutionThe surface area of the can is found by adding the areas of the twocircular bases and the rectangular side that surrounds them.The width, w, of the rectangle is the height of the can.The length, l, of the rectangle is equal to the circumference of the circle.a) To estimate, use approximate values:d 8 cm, w 10 cm, π 3.r2 meansArea of circle π r2r r 3 4 4 48How is the radius relatedto the diameter?There are two circles:2 48 96The area of the two circles is approximately 96 cm2.LiteracyLinkcircleradiuscentrediameterArea of rectangle l wWhat formulas could you (π d) wuse to find the circumference 3 8 10of a circle? 240The area of the rectangle is approximately 240 cm2.Estimated surface area area of two circles area of rectangle 96 240 340The estimated surface area is 340 cm2.5.4 Surface Area of a Cylinder MHR183
StrategiesDraw a Diagramb)Method 1: Use a NetDraw the net and label the measurements.topsidebottom7.5 cm11 cmThe diameter of the circle is 7.5 cm.Determine the radius.7.5 2 3.75The radius of the circle is 3.75 cm.If your calculator hasa π key, you can useit to get a moreaccurate answer.Find the area of one circle.Use 3.14 as anA π r2approximate valueA 3.14 3.752for π.A 44.15625The area of one circle is approximately 44.15625 cm2.Find the area of two circles.2 44.15625 88.3125The area of both circles is approximately 88.3125 cm2.Find the area of the rectangle using the circumference of the circle.A l wA (π d) wA 3.14 7.5 11A 259.05The area of the rectangle is approximately 259.05 cm2.Round youranswer at the end ofthe calculation.184MHR Chapter 5Calculate the total surface area.Surface area 88.3125 259.05 347.3625The total surface area is approximately 347.36 cm2.
Method 2: Use a Formula.Use this formula to find the total surface area of any cylinder.S.A. 2 (π r2) (π d h)This formula incorporates each shape and its areaS.A. 2 (3.14 3.752) (3.14 7.5 11)formula to find the surface area.2 (π r2) (π d) hS.A. 88.3125 259.05two circles circle arearectangle areaS.A. 347.3625formulaformula (length is theThe total surface area is 347.36 cm2, to thecircumference of a circle;nearest hundredth.width is the height ofthe cylinder)Calculate the surface area of thiscylinder to the nearest tenth of asquare centimetre.LiteracyLinkThe abbreviation S.A.is often used as ashort form for surfacearea.9 cm55 cmExample 2: Use the Surface Area of a CylinderCalculate the surface area of this totem pole, including the two circularbases. The pole stands 2.4 m tall and has a diameter of 0.75 m. Giveyour answer to the nearest hundredth of a square metre.SolutionThe cylinder has two circular bases.The area of one circle is:A π r2r d 2A 3.14 0.3752A 0.4415625The area of the circle isapproximately 0.4415625 m2.There are two circles, so the areaof both circles is approximately0.883125 m2.The side of the cylinder isa rectangle.The area of the rectangle is:A (π d) hA 3.14 0.75 2.4A 5.652The area of the rectangle isapproximately 5.652 m2.Calculate the total surface area.S.A. 0.883125 5.652S.A. 6.535125The total surface area is approximately 6.54 m2.Replace one dimensionwith the formula for thecircumference of a circle.Calculate the surface area of a cylindrical waste bucket without a lidthat measures 28 cm high and 18 cm in diameter. Give your answerto the nearest square centimetre.This metal totem polewas created by ToddBaker, Squamish Nation.It represents the Birth ofthe Bear Clan, with theprincess of the clan onthe top half and thebear on the bottom half.5.4 Surface Area of a Cylinder MHR185
The surface area of a cylinder is the sum of theareas of its faces. A net of a cylinder is made up of onerectangle and two circles. To find one of the dimensions of the rectangle,calculate the circumference of the circle.The length of this sideis the circumference ofthe circle C π ! d orC 2!π!r1.What are the similarities and differences between finding thesurface area of a prism and finding the surface area of a cylinder?2.Explain why you need to find the circumference of a circle to findthe surface area of a cylinder.5.For help with #3 to #7, refer to Examples 1 and 2 onpages 183–185.a)b)d 7 cm30 cmb)d 0.003 mwooden rod16 mEstimate the surface area of each cylinder.Then, calculate each surface area to thenearest tenth of a square centimetre.a)d 2.5 cm16 cmDraw a net for this cylinder.b) Sketch a different net forthis cylinder.3. a)4.Find the surface area of each objectto the nearest tenth of a square unit.r 10 cm22 cmflag pole6.Use the formulaS.A. 2 (π r2) (π d h) tocalculate the surface area of each object.Give each answer to the nearest hundredthof a square unit.a) d 2.5 cmb)d 5 cm10 cmYou can simplify the formula:S.A. 2 (π r2) (π d h) 2πr2 πdh186MHR Chapter 57 cm
7.8.Do you prefer to find the surface area ofa cylinder by using the sum of the area ofeach face or by using a formula? Give atleast two reasons for your choice.11.If each tennis ball has a diameter of 7 cm,calculate the amount of material needed tomake a can that holds three tennis balls.12.Coins can be stored in a plastic wrappersimilar to a cylinder. A roll of dimescontains 50 coins. Each dime has adiameter of 17.5 mm and a thickness of1 mm. Calculate the minimum surfacearea of the plastic wrapper.13.A paint roller in the shape of a cylinderwith a radius of 4 cm and a length of21 cm is rolled vertically on a wall.a) What is the length and width of thewet path after ten complete rolls?b) What area does the paint cover?Anu wants to re-cover the cylindrical stoolin his bedroom. How much material doeshe need if there is no overlap and he doesnot cover the bottom of the stool?d 42 cm32 cm9.Kaitlyn and Hakim each bought a tubeof candy. Both containers cost the sameamount. Which container required moreplastic to make?d 7 cmCANDY122 cmd 11 cmCANDY85 cm10.Paper towel is rolledaround a cardboardtube. Calculate theoutside surface areaof the tube.r 2 cmEach personproduces about1.59 kg of trash eachday. Most of this ispaper products.27.5 cmMATH LINKFor the cylindrical building you created in the MathLink on page 175, how much material do you need tocover the exterior walls and the roof of the building?Douglas J. Cardinal, one of the world’s mostacclaimed architects, uses his European, Blackfoot,and Ojibwa roots when designing buildings. He isknown for his design of The Canadian Museum ofCivilization in Gatineau, Québec, as well as anumber of buildings in Western Canada, such asTelus World of Science in Edmonton and FirstNations University of Canada in Regina.5.4 Surface Area of a Cylinder MHR187
a right triangular prism . The net can be folded to form the shape of a tent. triangular prism a prism with two triangular bases each the same size and shape . You can draw a net for an object by visualizing what it would look like if you cut along the edges and fl attened it o
2. Any data stored in the salesforce will be saved to objects. 3. It consist of Field (columns) and record (rows) 4. There are two types of objects a. Standard Objects. b. Custom Objects 4. Standard Objects: a. Objects which are created by the salesforce are called standard objects.
orthographic drawings To draw nets for three-dimensional figures. . .And Why To make a foundation drawing, as in Example 3 You will study both two-dimensional and three-dimensional figures in geometry. A drawing on a piece of paper is a two-dimensional object. It has length and width. Your textbook is a three-dimensional object.
instabilities that occurred in two dimensional and three dimensional simulations are performed by Van Berkel et al. (2002) in a thermocline based water storage tank. In two-dimensional simulations the entrainment velocity was 40% higher than that found in the corresponding three dimensional simulations.
An Example Dashboard An Integrated Problem Management Paradigm Use the graphics and integration capabilities of the Tivoli Enterprise Portal to provided custom dashboard views targeted for specific audiences – Technical views, Operational views, Alert management views, SME views, End to en
RAM/2013 TOTAL VIEWS: 20.8M GO PRO/2014 TOTAL VIEWS: 18.2M 1.4M VIEWS IN 2016 2M VIEWS IN 2016 1.7M VIEWS IN 2016 5M COMBINED VIEWS IN 20 16 Iconic ads continue to thrive on YouTube long past the moment. Old Spice's “The Man Your Man Could Smell Like” (2010), Ram's "Farmer" (2013) and GoPro and Red Bull’s “Red Bull Stratos - The
We introduce a new large-scale dataset that addresses three core research problems in scene understanding: de-tecting non-iconic views (or non-canonical perspectives [12]) of objects, contextual reasoning between objects and the precise 2D localization of objects. For many categories of objects, there exists an iconic view. For
v Using Templates to Re-Create Dimensional Objects.3-21 4 Querying Dimensional Objects Using SQL Querying Dimensional Data in SQL.4-1 Exploring the Shape of OLAP Views
Basics of Drafting. Describing an Angle Bracket. Orthographic Projection Orthographic drawings represent three dimensional objects in three separate views . the drawing individually. Pictorial A three dimensional pictorial is a drawing that shows an object's three principal planes, much as they would be
