1 Measurement. What you will learn. World s largest cylindrical aquarium. Australian Curriculum Measurement and Geometry Using units of measurement


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1 Austrlin Curriulum Mesurement nd Geometry Using units of mesurement hpter 1 Mesurement Wht you will lern Conversion of units Perimeter Cirumferene Are Are of irle Surfe re of prisms Surfe re of ylinder Volume of solids World s lrgest ylindril qurium Inside the Rdisson SAS hotel in Berlin is the world s lrgest ylindril qurium. Some of its mesurement fts inlude: Height: 25 m Dimeter: 11 m Volume of se wter: L Curved surfe re: 864 m 2 The trnsprent sing is mde from speil polymer tht is very strong nd n e mde nd delivered s one piee. Cylindril mesurement formuls re used to lulte the mount of polymer needed nd the volume of se wter it n hold.
2 2 Chpter 1 Mesurement Pretest 1 Nme these shpes. d e f g h 2 Write the missing numer. 1 km = m 1 m = m 1 m = mm d 1 L = ml e 0.5 km = m f 2.5 m = mm 3 Find the perimeter of these shpes. 3 m 4 Find the re of these shpes. 2 m 5 m 11 m 10 m 7 m 5 m 1.3 mm 2.5 mm 6 km 2.1 mm 5 Find the re of these tringles using A = 1 2 h. 4 m 2 m 4 m 7 m 3 km 6 Use C = π d nd A = π r 2 to find the irumferene nd re of this irle. Round to two deiml ples. 4 km 10 m d = 10, r = 5
3 Mesurement nd Geometry Conversion of units To work with length, re or volume mesurements, it is importnt to e le to onvert etween different units. Timer, for exmple, is widely used in uildings for frmes, roof trusses nd windows, to nme few things. It is importnt to order the orret mount of timer so tht the ost of the house is minimised. Although plns give mesurements in mm nd m, timer is ordered in metres (often referred to s linel metres), so we hve to onvert ll our mesurements to metres. Building house lso involves mny re nd volume lultions nd onversions. Let s strt: House plns All homes strt from pln, whih is usully designed y n rhitet nd shows most of the si fetures nd mesurements tht re needed to uild the house. Mesurements re given in millimetres BED 1 WIR BED 4 LIVING MEALS FAMILY KITCHEN GARAGE BED 3 WC BED 2 RUMPUS How mny edrooms re there? Wht re the dimensions of the mster edroom (BED 1)? Wht re the dimensions of the mster edroom, in metres? Will the rumpus room fit pool tle tht mesures 2.5 m 1.2 m, nd still hve room to ply? How mny rs do you think will fit in the grge? Wht do you think is going to over the floor of the kithen, mels nd fmily rooms?
4 4 Chpter 1 Mesurement Key ides To onvert units, drw n pproprite digrm nd use it to find the onversion ftor. For exmple: 1 km 1000 m 1 m m 100 m 1 m 3 1 km = 1000 m 1 m 2 = m 3 = = m 2 = 1000 mm 3 Conversions: Length km m m mm Are To multiply y 10, 100, 1000, et. move the deiml point one ple to the right for eh zero; e.g = km 2 m 2 m 2 mm Volume km 3 m 3 m 3 mm 3 To divide y 10, 100, 1000 et. move the deiml point one ple to the left for eh zero; e.g = Exerise 1A Understnding 1 Write the missing numers in these sentenes involving length. There re m in 1 km. There re mm in 1 m. There re m in 1 m. 1 km 1000 m 2 Write the missing numers in these sentenes involving re units. There re mm 2 in 1 m 2. There re m 2 in 1 m 2. There re m 2 in 1 km 2. 1 m 2
5 Mesurement nd Geometry 5 3 Write the missing numers in these sentenes involving volume units. There re mm 3 in 1 m 3. There re m 3 in 1 km 3. There re m 3 in 1 m 3. 1 m 3 Flueny Exmple 1 Converting length mesurements Convert these length mesurements to the units shown in the rkets. 8.2 km (m) 45 mm (m) Solution 8.2 km = = 8200 m Explntion 1 km 1000 m 1 km = 1000 m 45 mm = = 4.5 m 1 m 1 m = Divide if onverting from smller unit to lrger unit. 4 Convert the following mesurements of length into the units given in the rkets m (mm) 327 m (km) If onverting 834 m (m) d m (mm) to smller unit, multiply. e m (km) f m (m) Otherwise, divide. Exmple 2 Converting re mesurements Convert these re mesurements to the units shown in the rkets. 930 m 2 (m 2 ) 0.4 m 2 (mm 2 ) Solution Explntion 930 m 2 = = m 2 1 m m 1 m 2 = m 2 = = 40 mm m 1 m 2 = m 2 1 m 2 = = 100 mm 2
6 6 Chpter 1 Mesurement 1A 5 Convert the following re mesurements into the units given in the rkets m 2 (mm 2 ) 0.5 m 2 (m 2 ) 1 m 2 = 100 mm 2 5 km 2 (m 2 ) d mm 2 (m 2 ) 1 m 2 = m 2 e 537 m 2 (mm 2 ) f m 2 (m 2 ) 1 km 2 = m 2 Exmple 3 Converting volume mesurements Convert these volume mesurements to the units shown in the rkets m 3 (mm 3 ) 4300 m 3 (m 3 ) Solution Explntion 3.72 m 3 = = 3720 mm 3 1 m 3 1 m 3 = = 1000 mm m 3 = = m m 1 m m 1 m 3 = m = m 3 6 Convert these volume mesurements into the units given in the rkets. 2 m 3 (mm 3 ) 0.2 m 3 (m 3 ) 5700 mm 3 (m 3 ) d km 3 (m 3 ) e m 3 (km 3 ) f m 3 (m 3 ) 1 m 3 = 1000 mm 3 1 m 3 = m 3 1 km 3 = m 3 7 An thlete hs ompleted 5.5 km run. How mny metres did the thlete run? Prolemsolving nd Resoning
7 Mesurement nd Geometry 7 8 Determine the metres of timer needed to onstrut the following frmes. 240 m 200 m 60 m 60 m60 m60 m60 m60 m 60 m 140 m 40 m 60 m 9 Find the totl sum of the mesurements given, expressing your nswer in the units given in the rkets. 10 m, 18 mm (mm) 1.2 m, 19 m, 83 mm (m) Convert to the units in rkets. Add up 453 km, 258 m (km) d 400 mm 2, 11.5 m 2 (m 2 ) to find the sum. e 0.3 m 2, 251 m 2 (m 2 ) f km 2, 9 m 2, m 2 (m 2 ) g mm 3, 2.5 m 3 (mm 3 ) h km 3, m 3 (m 3 ) 10 A snil is moving t rte of 43 mm every minute. How mny entimetres will the snil move in 5 minutes? 11 Why do you think tht uilders mesure mny of their lengths using only millimetres, even their long lengths? Speil units 12 Mny units of mesurement prt from those relting to mm, m, m nd km re used in our soiety. Some of these re desried here. Length Inhes 1 inh 2.54 m = 25.4 mm Feet 1 foot = 12 inhes m Miles 1 mile km = 1609 m Are Squres 1 squre = 100 squre feet Hetres (h) 1 hetre = m 2 Volume Millilitres (ml) 1 millilitre = 1 m 3 Litres (L) 1 litre = 1000 m 3 Convert these speil mesurements into the units given in the rkets. Use the onversion informtion given erlier to help. 5.5 miles (km) 54 inhes (feet) 10.5 inhes (m) d 2000 m (miles) e 5.7 h (m 2 ) f 247 m 3 (L) g 8.2 L (ml) h 5.5 m 3 (ml) i 10 squres (sq. feet) j 2 m 3 (L) k 1 km 2 (h) l ml (m 3 )
8 8 Chpter 1 Mesurement 1.2 Perimeter Perimeter is mesure of length round the outside of shpe. We lulte perimeter when ordering eiling ornies for room, or mterils for fening pddok or uilding television frme. Let s strt: Lshped perimeters This Lshped figure inludes only right (90 ) ngles. Only two mesurements re given. Cn you figure out ny other side lengths? Is it possile to find its perimeter? Why? 10 m 13 m Key ides Perimeter is the distne round the outside of twodimensionl shpe. To find the perimeter we dd ll the lengths of the sides in the sme units. P = = 24 m 7 m 8 m 4 m Perimeter The totl distne (length) round the outside of figure 5 m If two sides of shpe re the sme length they re lelled with the sme mrkings. P = 2x + y + z x z y
9 Mesurement nd Geometry 9 Exerise 1B Understnding 1 Write the missing word: The distne round the outside of shpe is lled the. 2 Write down the vlue of x for these shpes. 6 x 7.1 x x 4.3 Flueny Exmple 4 Finding perimeters of si shpes Find the perimeter of these shpes. 2 m 3 m 3 m 3.5 m 4 m 5 m 4.5 m Solution Perimeter = = 12.5 m Perimeter = = 18.5 m Explntion Add ll the lengths of the sides together. Three lengths hve the sme mrkings nd re therefore the sme length. 3 Find the perimeter of these shpes. 3 m 4 m 5 m 4 m 6 m 7 m 6 m 5 km 3 km Sides with the sme mrkings re the sme length. d 3 m e f 6.4 m 2.5 m 2.5 m
10 10 Chpter 1 Mesurement 1B 4 Find the perimeter of these shpes. 1.3 m 1.2 m 2.4 m 1.8 m 8 mm 22 mm 18 mm 17 mm d 2 m 220 m 7 m 185 m 3 m e 0.5 km f 12 m 34 m 32 m 2.6 km Prolemsolving nd Resoning Exmple 5 Finding missing side length Find the vlue of x for this shpe with the given perimeter. 4.5 m 2.1 m P = 11.9 m 3.4 m x m Solution x = x = 11.9 x = 1.9 Explntion All the sides dd to 11.9 in length. Simplify. Sutrt 10 from oth sides.
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