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1 topic 17 s of 3-D shapes 17.1 Overview Why learn this? Knowlege of geometry an mathematis is essential for unerstaning how 3-imensional (3-D) spaes work. hree-imensional shapes exist all aroun us from a ylinrial water ottle to prism shape oxes, retangular playing fi els, an spherial an oval shape alls. Drawing a 3-imensional shape epens on the view you wish to show. Designs an ieas aout 3-imensional shapes an e ommuniate using 2-imensional rawings. What o you know? 1 think List what you know aout reaing sales. Use a thinking tool suh as a onept map to show your list. 2 PaIr Share what you know with a partner an then with a small group. 3 share As a lass, reate a thinking tool suh as a large onept map that shows your lass s knowlege of sales. Learning sequene 17.1 Overview 17.2 Sales an house plans 17.3 Plans an views 17.4 Isometri rawing 17.5 eview ONLINE ONLY 642 Maths Quest 7

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3 Digital os SkillSHEE Metri units of length o-6546 SkillSHEE eaing sales o Sales an house plans Unerstaning sales A sale on a map or plan esries the ratio etween the istane on the map or plan an the atual istane on the Earth s surfae. A sale may e written several ways. A ratio suh as 1 : means that 1 m on a map or plan represents a istane of m on the Earth, or 1 mm on the map or plan represents mm on the Earth, et. A statement suh as 1 m 500 km means that 1 m on the map or plan represents a istane of 500 km on the Earth. A graphial ar sale, suh as the one shown in Worke example 1, an e use. In this ase, we nee to measure the length of the ar to etermine the sale ratio. WorKeD example 1 a he sale on a house plan is 1 : How many metres oes a length of 1 m on the map represent? Write the sale 1 m 5000 m as a ratio sale. A map shows a sale of 1 m 1500 m. What istane is represente y 18 mm on the map? Use the following graphial sale to etermine the istane that 1 m on the map represents. think a 1 Use the ratio to a the same units to oth sies. Sine the answer asks for m, use this unit. 2 Bring the length to an appropriate unit. In this ase, the answer is require in metres kilometres WrIte a 1 : 2000 is the same as: 1 m 2000 m 2000 m = ( ) m = 20 m So, 1 m 20 m. 3 Write the answer. 1 m on the map represents a length of 20 m in reality. 1 Convert the groun units to the same as those of the map m = ( ) m = m 2 Write the sale as a ratio. So, 1 m 5000 m is the same as 1 m m. Expresse as a ratio, this is 1 : Write a statement explaining this sale. 2 Change the question istane to the same units as those for the map. 1 m 1500 m means that 1 m on the map represents a istane of 1500 m. 18 mm = (18 10) m = 1.8 m 644 Maths Quest 7

4 3 Multiply y this sale fator. 1.8 m represents ( ) m, whih is 2700 m or 2.7 km. 1 Measure the length of the ars with a ruler. 2 elate this measurement to the length shown in the sale. Sometimes it is neessary to o the reverse, an onvert from a real length to a plan measurement. House plans Whenever a house is eing onstrute, floor plans are supplie to the uiler so that the footings, walls, roof et. are all plae in the orret positions an are the orret length. he sale of the plan is generally given as a ratio. his enales us to alulate all imensions within the house. he ars measure 3.5 m. 3 Write as a sale. 3.5 m 15 km 4 Calulate a 1 m map istane an write the answer. WorKeD example 2 his represents a length of 15 km. So, 1 m 15 km 35 1 m on the map represents a istane of 4.3 km. he length of a wall for a partiular house is 12 m. If the sale of a house plan is 1 : 200, what length, on the plan, woul represent the atual length of the wall? think 1 Write the sale as a ratio using units of m. 2 Convert the atual length from m to m units. 3 Divie the atual length y 2 to fin how many lots of 2 m there are in 12 m. 4 Multiply oth sies of the sale y this sale fator then simplify. WrIte 1 : 200 means that 1 m on the plan represents an atual length of 200 m. 1 m 200 m 200 m = ( ) m = 2 m So 1 m on the plan represents an atual length of 2 m. 1 m 2 m 1 2 m 2 m = 6 1 m 6 2 m 6 6 m 12 m 5 Answer the question. he length of the wall on the house plan woul e 6 m. opi 17 s of 3-D shapes 645

5 WorKeD example 3 Below is a plan for a house. Kithen/Dining Lounge a Calulate the imensions of the house. Calulate the area of the lounge room. think a 1 Measure the length an with of the house on the plan. 2 Multiply eah of these measurements y 100. WrIte a WC Bathroom Be 3 Be 2 Be 1 Length of house on plan = 12 m With of house on plan = 10 m Sale 1 : 100 Atual length of house = 12 m 100 = 1200 m = 12 m Atual with = 10 m 100 = 1000 m = 10 m 3 Write your answer. he imensions of the house are 12 m y 10 m. 1 Measure the length an with of the lounge room on the plan. 2 Multiply eah of these measurements y 100. Length of lounge room on plan = 6 m With of lounge room on plan = 6 m Atual length of lounge room = 6 m 100 = 600 m = 6 m Atual with of lounge room is also 6 m. 646 Maths Quest 7

6 3 Calulate the area of the lounge room. In aition to a floor plan, a uiler nees to know what the house will look like if it is viewe from the front, ak an sies. hese plans are alle elevations. hese are also rawn to sale. With an unerstaning of house plans, you shoul now e ale to raw plans of ojets familiar to you, suh as your home, eroom or lassroom. It is important to inlue a sale with eah plan. Sometimes a legen is also appropriate. Exerise 17.2 Sales an house plans InDIvIDuaL PatHWays A = 6 2 = 36 m 2 4 Write your answer. he area of the lounge room is 36 m 2. WorKeD example 4 he iagram at right shows the front elevation of a house. a Calulate the height of the eaves on the lower sie of the house. Measure the angle of the pith of the roof. think a 1 Measure the height on the plan for the lower sie of the house. 2 Multiply the plan measurement y 100. WrIte a Height on the plan = 3.5 m Atual height = 3.5 m 100 = 350 m = 3.5 m 3 Write your answer. he height of the eaves is 3.5 m. 1 Measure the angle that the slope of the roof makes with the horizontal. Angle to horizontal = 45 Sale 1 : Write your answer. he angle of the pith of the roof is 45. PraCtIse Questions: 1, 2, 3, 4, 5, 6, 7, 8, 14 ConsoLIDate Questions: 1, 2, 3, 4, 5, 6, 7a,, e, g, 8, 10a,, 12, 14, 15 master Questions: 1, 2, 3, 4, 5, 6, 7a,, h, 8, 9, 10, 11, 12, 13, 14, 15 relection Why is it important to show the position of north on a plan? Iniviual pathway interativity int-4391 opi 17 s of 3-D shapes 647

7 measurement AND geometry LUENCY 1 WE1 ewrite the following ratio sales in the form 1 m using the most appropriate units. a 1 : 10 1 : : : e 1 : f 1 : 5000 g 1 : h 1 : 400 i 1 : j 1 : Write the following as ratio sales. a 1 m 20 m 1 m m 1 m 10 m 1 m 200 m e 1 m 5 km f 1 m 50 km g 1 m 5.5 km h 2 m 2 km i 2 m 2.5 km j 3 m 6 km 3 WE2 he sale of a town plan is given as 1 : Use this to fin the istanes on the plan etween: a two intersetions that are 1 km apart two epartment stores that are 200 m apart an airport an a motel that are 15 km apart a servie station an a ank that are 2.5 km apart e the northern an southern extremities, whih are 22 km apart f two shops that are 500 m apart. 4 WE3 Below is the site plan for a lok of lan. a What are the imensions of the lok of lan? What are the imensions of the house? N House Garage She Driveway Garen e Garen e Sale 1 : Maths Quest 7

8 measurement AND geometry 5 A house plan is shown elow. Lounge Be 3 Be 4 amily Be 1 Be 2 oilet Bathroom a Calulate the imensions of the house. What are the imensions of the lounge room? Whih eroom is the largest? What are its imensions? 6 WE4 Below is the front elevation of a house, rawn to sale. Pantry Launry Kithen Sale 1 : 150 a Calulate the height of the peak of the roof. Calulate the height of the eaves. Measure the angle of the pith of the roof. Sale 1 : 100 opi 17 s of 3-D shapes 649

9 measurement AND geometry UNDESANDING 7 If a sale of 1 : 50 is use to make eah of the following rawings: a what woul e the with of the rawing of a house whih is 25 m wie what woul e the height of the rawing of a man who is 2 m tall what woul e the imensions of the rawing of a retangular pool 50 m y 20 m what woul e the imensions of the rawing of a tale 4 m y 1.5 m e what is the atual height of a tree whose height in the rawing is 10 m f what is the atual length of a truk whose length in the rawing is 25 m g what are the imensions of a television set whose imensions on the rawing are 10 mm y 8 mm h what are the imensions of a e whose imensions on the rawing are 4.5 m long y 3 m wie y 1.2 m high? 8 eferring to the following plan of the house, fin: Lounge Garage Kithen/Living Linen Launry Bath WC Beroom 1 Beroom 3 Beroom 2 Sale 1 : 200 a the imensions of the lounge the with of the hallway the length of the garage the floor area of the kithen/living room e the total floor area of the largest eroom. (Hint: Use a ruler to fin the require lengths on the plan first.) 9 rae the front elevation of the following house into your ook. On your iagram write all lengths an angles neessary for the onstrution of the house. Sale 1 : he following iagrams are representations of houses with a variety of roof types. Draw a plan of the south an east elevations of these houses. he iretion of north is given. 650 Maths Quest 7

10 measurement AND geometry a Gale roof Hip roof N N Boxe gale roof N N Gamrel (a roof omining the aition of small gales to a hip roof) 11 Choose an area whih is familiar to you, suh as your home, eroom, lassroom or shool grouns. Draw a plan of your area. Inlue a sale an a legen. Don t forget to show the northerly iretion. EASONING 12 A retangular room has with 3 m an length 5 m. a What are the imensions of the iagram on a sale of 1 : 100? What is the area of the retangle on the iagram? he iagram has een enlarge so that the imensions of the new iagram are oule the imensions of the first iagram. What is the area of the retangle on the new iagram? Calulate the area of a retangle with imensions three times igger than the original iagram. e How oes enlargement affet the area of a shape? 13 What woul happen to the value of an area of a surfae if its imensions were reue y a fator n? Prolem Solving 14 Athena the artist paints portraits. or her present sujet, Seth, she uses the following measurement relationships. Seth s arm span is the same length as his height. he length of Seth s han is one-tenth of his height. he istane aross Seth s shoulers is one-quarter his height. opi 17 s of 3-D shapes 651

11 What is the relationship etween Seth s arm span, the length of his han an the istane aross his shoulers? 15 Mikaela wants to uy a new frige that is 800 mm eep an 1 m wie. She is restrite, though, y the kithen spae. he plae for the frige, on the iagram, has imensions 1.5 m epth an 2 m with. If the sale of the rawing is 1 : 50, will this frige fit in the spae given? State the atual imensions of the frige spae Plans an views Prisms CH HaLLenge 17.1 A prism is a 3-imensional figure that an e ut into parallel slies or ross-setions that are iential in size an shape. Ojets or uilings are often onstrute y omining prisms. Plans an views An ojet an e viewe from ifferent angles. Arhitets an raftspersons often raw plans of uiling sites an various ojets when viewe from the front, the sie or the top. he front view, or front elevation, is what you see if you are staning iretly in front of an ojet. he sie view, or sie elevation, is what you see if you are staning iretly to one sie of the ojet. You an raw the left view or the right view of an ojet. he top view, or ir s eye view, is what you see if you are hovering iretly over the top of the ojet looking own on it. WorKeD example 5 he following ojet is mae from 4 ues. Draw plans of it showing: a the front view the right view the top view. 652 Maths Quest 7

12 think a Make this shape using ues. Plae the shape at a onsierale istane an look at it from the front (this way you an see only the front fae of eah ue). Draw what you see. (Or simply imagine looking at the shape from the front an raw what you see.) Look at your moel from the right, or imagine that you an see only the right fae of eah ue an raw what you see. Look at your moel from the top, or imagine that you an see only the top fae of eah ue. Draw what you see. DraW igures suh as the one in Worke example 5 an e rawn using isometri ot paper. his will help to give the 3-imensional perspetive of the ojet. WorKeD example 6 Draw: i the front view ii the right view iii the top view of this soli. think 1 in an ojet of similar shape, or visualise the ojet in your hea. 2 Whether viewe from the front, or from the right of the ojet, the ylinrial shaft will appear as a long thin retangle. he irular iss will also e seen as a pair of iential retangles. So the front view an the right view are the same. 3 When the ojet is viewe from aove, all we an see is the flat surfae of the top is; that is, a large an a small irle with the same entre. (Note that suh irles are alle onentri.) a DraW view ight view op view view ight view op view opi 17 s of 3-D shapes 653

13 WorKeD example 7 he front, right an top views of a soli are shown. Use ues to onstrut the soli. think view 1 Use ues to onstrut the soli. ight view op view 2 Chek arefully that your soli mathes eah of the 3 views you are given. Make ajustments if neessary. ConstruCt Perspetive rawing A 2-imensional representation of a 3-imensional ojet an e mae using a singlepoint perspetive. his shows the ojet as it appears to the eye in reality. When we look at a piture of a sene, the ojets seem to onverge or move towars a point in the istane. his point is alle a vanishing point. WorKeD example 8 Construt a perspetive rawing of the retangular prism shown. think 1 Draw the front fae of the prism as a retangle. 2 ake a vanishing point in the istane ehin the ojet an slightly to the right. Draw otte lines from this point to the orners of the front fae of the prism. DraW 3 On these otte lines, make the following markings. Draw the top ege of the ak fae parallel to the top ege of the front fae. Also raw the right ege of the ak fae parallel to the right ege of the front fae. 654 Maths Quest 7

14 4 Join the top an right-sie verties of the front fae to the orresponing verties of the ak fae. Exerise 17.3 Plans an views InDIvIDuaL PatHWays PraCtIse Questions: 1, 2, 3, 4, 5, 6, 11, 12 ConsoLIDate Questions: 1, 2, 3, 4, 5, 6, 9, 11, 12 Iniviual pathway interativity int-4392 master Questions: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 LuenCy 1 WE5 he following ojets are mae from ues. or every ojet raw the plans, showing the front view, the right view an the top view. (You may wish to use a set of ues or uiling loks to help you.) a g e h f i relection Why is the tehnique of perspetive rawing frequently use in artisti paintings? opi 17 s of 3-D shapes 655

15 2 WE6 Draw the front, right an top views of eah soli shown. a 3 WE7 he front, right an top views of a soli are shown. In eah ase, use ues to onstrut the soli. a view ight view op view view ight view view ight view op view view ight view op view op view 4 WE8 Construt a perspetive rawing of a ue. 656 Maths Quest 7

16 understanding 5 MC he front, right an top views of a soli are shown. Whih of the given rawings oul represent the soli? view ight view op view Interativity Plans, elevations an ross-setions int-0009 a D e 6 a What shape is the top view of a telephone pole? What shape is the top view of the Melourne Criket Groun? What shape is the sie view of a uket? What shape is the top view of a ar? 7 a Draw the sie view of this pool tale. Draw the front view of your house (seen from the street). Draw the sie view of an eletri kettle. Draw the top view of your television set. 8 A shape is mae using only 4 ues. Its front view, right view an top view are shown. C view ight view op view a Is it possile to onstrut this soli? Desrie or raw what this soli woul look like. reasoning 9 Explain why a 3-D ojet requires three to six iagrams to learly represent its views. 10 How many ojets an you onstrut using the top view shown? Explain your answer with the use of iagrams. ProLem solving 11 Draw top, front an sie views for the 3-D ojets given. opi 17 s of 3-D shapes 657

17 12 Draw top, front an sie views for the 3-D ojets given. WorKeD example 9 irst opy the inomplete figure (igure 1) onto isometri ot paper. Complete the isometri rawing of the ojet (igure 2). think CH HaLLenge Isometri rawing When working with 3-imensional moels an esigns, it is often useful to have the esign or moel rawn on paper (that is, in 2 imensions). An isometri rawing is a 2-imensional rawing of a 3-imensional ojet. his piture shows an arhitet s rawing of a eah hut an environs in isometri view superimpose on the atual hut. Arhitets an raftspersons often use isometri rawings to give their lients a lear piture of the propose esign. Stuy the ojet an ientify the lines that have alreay een rawn. ill in the missing lines on your isometri rawing to math the ojet. igure 1 igure 2 DraW 658 Maths Quest 7

18 WorKeD example 10 Draw the following ojet on isometri ot paper. (You oul onstrut it first from a set of ues.) think Exerise 17.4 Isometri rawing InDIvIDuaL PatHWays PraCtIse Questions: 1, 2, 3, 4, 5, 8, 11 ConsoLIDate Questions: 1, 2, 3a,, 4, 5, 6, 8, 9, 11 Iniviual pathway interativity int-4393 master Questions: 1, 2, 3,, 4, 5, 6, 7, 8, 9, 10, 11 LuenCy 1 WE9 Copy the following figures onto isometri ot paper an omplete the isometri rawing of the ojets shown. a 1 Use ues to make the ojet shown (optional). Draw the front fae of the ojet. he vertial eges of the 3-imensional ojet are shown with vertial lines on the isometri rawing; the horizontal eges are shown with the lines at an angle (y following the ots on the gri paper). 2 Draw the left fae of the ojet. 3 A the top fae to omplete the isometri rawing of the ojet. DraW relection How oes isometri ot paper turn two-imensional lines into a three-imensional image? opi 17 s of 3-D shapes 659

19 measurement AND geometry 2 WE10 Draw eah of the following ojets on isometri ot paper. (You might wish to make them first from a set of ues.) a UNDESANDING 3 Construt the following letters using ues, an then raw the solis on isometri ot paper: a the letter with 5 ues the letter L with 7 ues the letter E with 10 ues the letter H with 7 ues. 4 Draw these ojets, whose front (), right () an top () views are given, on isometri ot paper. a 5 Draw the front, right an top views of these ojets. a 6 Draw the following figure on isometri ot paper. 660 Maths Quest 7

20 7 Draw a seletion of uilings from this photograph of a ity skyline on isometri ot paper. reasoning 8 On the same isometri ot paper raw the two wooen oxes shown. 9 Draw top, front an sie views of the ojet shown in the following isometri rawing. opi 17 s of 3-D shapes 661

21 Digital o WorkSHEE 17.1 o-6561 ProLem solving 10 Sam has a set of wooen ue loks he uses to uil ifferent shapes. His sister Chris hallenge him to see how many ifferent ways he oul stak 4 ues. He an only stak them on top of eah other or sie y sie not one ehin the other. he arrangements must e ifferent an not simply a mirror image or rotation of another shape. Draw the ifferent arrangements possile. 11 Jonah is uiling a rik wall as shown in the following photograph. Draw this part of the wall on isometri ot paper. 662 Maths Quest 7

22 measurement and geometry 17.5 eview he eview ontains: lueny questions allowing stuents to emonstrate the skills they have evelope to effiiently answer questions using the most appropriate methos Prolem solving questions allowing stuents to emonstrate their aility to make smart hoies, to moel an investigate prolems, an to ommuniate solutions effetively. A IO Language EV sale fator sie view top view vanishing point SA M PL int-3177 legen map sale perspetive plan ratio E int-2743 AL U int-2742 onverge imensions elevations front view isometri rawing Downloa the eview questions oument from the links foun in your ebookplus. N A summary of the key points overe an a onept map summary of this hapter are availale as igital ouments. eview questions N LY he Maths Quest eview is availale in a ustomisale format for stuents to emonstrate their knowlege of this topi. O ONLINE ONLY Link to assesson for questions to test your reainess or learning, your progress as you learn an your levels o ahievement. Link to SpyClass, an exiting online game omining a omi ook style story with prolem-ase learning in an immersive environment. assesson provies sets of questions for every topi in your ourse, as well as giving instant feeak an worke solutions to help improve your mathematial skills. Join Jesse, oy an Dan an help them to takle some of the worl s most angerous riminals y using the knowlege you ve gaine through your stuy of mathematis. opi 17 s of 3-D shapes 17sOf3-DShapes.in /05/16 12:36 PM

23 <InvestIgatIon> or rich task or <measurement and geometry> or PuZZLe rich task Making a trunate otaheron A trunate otaheron is forme when the verties of an otaheron are ut off. runate means to ut off. New square faes form when the verties are ut off, prouing the trunate otaheron as shown in fi gure 3. Copy the net that appears in fi gure 1 onto stiff aroar. Cut along the soli outer lines, taking are not to ut the tas off. ol upwars along the otte lines. he est way to fol is to rule a pen along the otte lines fi rst an then fol upwars. Starting at the entral hexagon (laelle A), fol eah of the surrouning shapes upwars. he 3-imensional shape will egin to take shape. Glue or stiky-tape the tas to the insie of eah ajoining fae. 664 Maths Quest 7

24 Carefully examine the net of the trunate otaheron shown in figure 1. 1 What shapes oes it ontain? 2 How many of eah shape are there? 3 When you have onstrute your soli, state the numer of faes, verties an eges assoiate with the shape. A smaller version of your net is shown in figure 2, along with the soli form (figure 3). igure 2 igure 1 4 Choose a olour pattern, using at least three ifferent olours for your net. Show how it will appear on the three-imensional soli. 5 Investigate other asi three-imensional shapes an try to onstrut them using straws. Provie a name an a plan of your shapes nets. A igure 3 opi 17 s of 3-D shapes 665

25 <InvestIgatIon> measurement and or geometry rich task or <measurement and geometry> or PuZZLe CoDe PuZZLe Who invente the motion piture in 1891 an what was it alle? Math the numer esie eah plan an sie view of a soli with the letter esie its name to fin the puzzle s answer oe Plan Plan 5. Plan 6. iretion Plan Plan iretion Plan iretion iretion iretion 7. Plan iretion Plan iretion Plan Plan Plan Plan iretion iretion iretion iretion A. Cyliner C. Pentagonal Pyrami D. Hemisphere E. Otagonal Prism H. Sphere I. riangular Prism K. Cuoi M. riangular Pyrami N. Hexagonal Pyrami O. Hexagonal Prism P. Pentagonal Prism 13. Plan S. Square Pyrami. Cue iretion iretion Maths Quest 7

26 Ativities 17.2 sales an house plans Digital os SkillSHEE (o-6546) Metri units of length SkillSHEE (o-6547) eaing sales? Interativity IP interativity 17.2 (int-4391) Sales an house plans 17.3 Plans an views Interativities Plans, elevations an ross-setions (int-0009) IP interativity 17.3 (int-4392) Plans an views 17.4 Isometri rawing Digital o WorkSHEE 17.1 (o-6561) to aess eookplus ativities, log on to Interativity IP interativity 17.4 (int-4393) Isometri rawing 17.5 review Interativities Wor searh (int-2742) Crosswor (int-2743) Suoku (int-3177) Digital os opi summary (o-10748) Conept map (o-10749) opi 17 s of 3-D shapes 667

27 measurement AND geometry Answers OPIC 17 s of 3-D shapes 17.2 Sales an house plans 1 a 1 m 10 m 1 m 1 m 1 m 10 m 1 m 100 m e 1 m 1 km f 1 m 50 m g 1 m 600 m h 1 m 4 m i 1 m 7.5 km j 1 m 22 km 2 a 1 : 20 1 : : : e 1 : f 1 : g 1 : h 1 : i 1 : j 1 : a 1 m 2 mm 15 m 2.5 m e 22 m f 5 mm 4 a 20 m 25 m 10 m 15 m 5 a 18 m 12 m 6.75 m 4.5 m Be m 4.5 m 6 a 8.5 m 3.5 m 40 7 a 50 m 4 m 100 m 40 m 8 m 3 m e 5 m f 12.5 m g 50 m 40 m h 2.25 m 1.5 m 0.6 m 8 a 6 m 4 m 1 m 6.8 m 24 m 2 e 12 m 2 9 Chek with your teaher. 10 Chek with your teaher. 11 Chek with your teaher. 12 a 3 m an 5 m 15 m 2 60 m m 2 e If the imensions oule, the area eomes four times larger. If the imensions are three times igger, the area eomes nine times larger. If the imensions are enlarge y a fator n, the area is enlarge y a fator n If the imensions were reue y a fator n, the area woul e reue y a fator n Seth s arm span is 10 times the length of his han an 4 times the istane aross his shoulers. 15 No. Depth is 750 m, with is 1 m. Challenge 17.1 he towns were 5 m apart on the original map. hey are atually 375 km apart Plans an views 1 a g 2 a 3 a h an 4 i e f 5 D 6 a Cirle Oval rapezium etangle 7 a Various answers 668 Maths Quest 7

28 measurement AND geometry 8 a It woul e iffiult to onstrut this soli Isometri rawing 1 a he soli woul look like the one shown. he 4th ue is ehin the front ottom ue, resting on the surfae. he two top ues have no ues supporting them. 9 Usually a 3-D ojet will require only 3 views as normally the front an ak faes are iential, the top an ottom faes are iential, an the left an right faes are iential. here are instanes when an ojet has no iential faes. In these situations all views have to e rawn in orer to show the etails of eah fae. 10 An infinity of shapes eause there are no restritions on the other two views op view view Sie view op view view Sie view op view view Sie view op view view Sie view Challenge 17.2 view ight view 2 a 3 a 4 a op view opi 17 s of 3-D shapes 669

29 measurement AND geometry 5 a an sie views 6 7 Chek with your teaher. 8 9 op view Investigation ih task 1 Hexagons an squares 2 8 hexagons an 6 squares 3 aes = 14, verties = 24, eges = 36 4 eaher to hek 5 eaher to hek Coe puzzle homas Eison, Kinetosope 670 Maths Quest 7

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