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Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
The International System of Units, abbreviated SI, (from the French le Système International d’unités) is theofficial system of measurement in Canada.
Length
1 kilometre (km) = 1000 metres (m)100 centimetres (cm) = 1 metres (m)10 millimetres (mm) = 1 centimetre (cm)
Conversions
1 km = 1000 m or 1 m = 0.001 km100 cm = 1 m or 1 cm = 0.01 m10 mm = 1 cm or 1 mm = 0.1 cm
The advantage of the metric system is that it is easy to convert from one unit to another. That is because the metric system is based on the number 10.
The basic unit of measure is the metre. The metre is used for expressing the dimensions of larger objects, such as the height of a building. The millimetre is used to measure small distances, especially in science andindustry, such as the thickness of a pane of glass. The kilometre is used for large distances, such as the distance between two cities.
Find the missing lengths.
a) 1 km = cm
b) 12.3 m = mm
►Solution: a) 1 km = 1000 m, 1 m = 100 cm
then 1000 m = 1000 # 1 m = 1000 # 100 cm = 100 000 cm
b) 1 m = 100 cm, 1 cm = 10 mm
then 12.3 m = 12.3 # 1 m = 12.3 # 100 cm = 1230 cm
and 1230 cm = 1230 # 1 cm = 1230 # 10 mm = 12 300 mm
Example 1
Metric Systems1.1
♦ 5Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.1 Exercise Set
1. Use: mm, cm, m or km to complete the sentence.
a) A ruler is 25 long. b) Vancouver is 2237 from Winnipeg.
c) A loonie is 2 thick. d) The football players ran 7 for a first down.
e) This book is 3 thick. f) The girl is 1.6 tall.
g) The marathon run is 42.3 long. h) The small bug is 8 long.
i) Niagara Falls is 0.053 high. j) A 4 litre milk container is 26 high.
k) A $2.00 coin is 28 in diameter. l) A table is 78 high.
m) A window pane is 8 thick. n) A fir tree is 42 high.
o) A plane is flying at a height of 7.3 . p) Mt. McKinley is 6149 above sea level.
♦ 6Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
2. Find the equivalent measurement. Do as many as possible mentally.
a) 1 m = cm b) 1 cm = m
c) 1 km = m d) 1 m = km
e) 1 m = mm f) 1 mm = m
g) 1 km = cm h) 1 cm = km
i) 1 km = mm j) 1 mm = km
♦ 6Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
3. Find the equivalent measurement.
a) 36.3 mm = cm b) 3 km = cm
c) 500 m = mm d) 500 mm = km
e) 8.26 cm = m f) 7.2 mm = m
g) 0.3 km = m h) 0.02 km = mm
i) 63 cm = km j) 4200 mm = km
k) 40 km = mm l) 0.043 km = mm
♦ 7Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. Complete the table.
Object mm cm m kma) Width of sheet of paper
21.7
b) Length of sheet of paper0.28
c) Length of MP3 player92.3
d) Height of CN tower0.553
e) Thickness of phone book3.8 cm
f) Width of library card53.2
g) Length of the Lions Gate Bridge 182300
h) Length of Canadian football field 146.3
i) Thickness of graphic calculator18.2
j) Width of bedroom0.0038
♦ 7Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
5. Each sentence is incorrect. Move or insert a decimal point to make the sentence correct.
a) The average female height is 1.63 cm.
b) The length of a Persian rug is 0.37 m.
c) A stack of 20 loonies is 391 cm high.
d) The average foot is 2.8 mm long.
e) The highest mountain in Canada is Mt. Logan, Yukon at 59.56 m.
f) The longest river in Canada is the Mackenzie at 4241 m.
g) The highest waterfall in Canada is Della Falls, BC at 4.4 m.
Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
6. Add.
a) 18 m + 1.6 km + 235 cm m
b) 315 mm + 87 cm + 4.2 m cm
c) 0.2 m + 47 cm + 86 mm mm
d) 4.3 km + 64.3 m + 128 cm km
e) 1.8 km + 9.2 m + 7.3 cm + 5.6 mm mm
♦ 8Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
7. The Trans-Siberian rail is the longest in the world 8. The subway system in New York is 371 000 metres at 944 km. How many centimetres is the track? long, and the subway system in London is 415 km long. How many metres longer is the London system than the New York System?
9. A virus in the human body is 0.000 000 0026 metres 10. The Quingzang railroad in Tibet is the highest in diameter. How many millimetres in diameter is railroad in the world at 5072 metres high. the virus? How many kilometres high is the railroad?
11. The Tour de France bicycle race is 3600 km long 12. The longest certified ultra marathon in the world is and lasts 3 weeks. How many metres are travelled is a race that covers 209 200 metres. How many in the 3 week race? kilometres is this race?
♦ 9Lambrick Park Secondary
Section 1.1 - Metric Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
13. The record for the longest swim is 5268 km, set by 14. The record for the longest long jump was set by Martin Strel in the Amazon River over the course Mike Powell of the USA, in 1991. His jump of 66 days. How many kilometres did he swim per measured 8950 mm. How many metres long was day? his jump?
15. The world record for the pole is 6.14 m for men, 16. The world’s tallest man is 246.5 cm in height, and 506 cm for women. How many cm higher is and the world’s shortest man is 0.5715 m in height. the men’s record than the women’s record? What is the difference in their height in cm?
♦ 9Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
TheimperialunitofmeasureismainlyusedintheUnitedStates,butinCanadaitisstillusedforcertain measurements.Lumber,plywoodandnailsareexamplesofmanufactureditemsthatuseimperialunits.
Length
12inches(in) = 1foot(ft) 3feet(ft) = 1yard(yd) 36inches(in) = 1yard(yd) 1760yards(yd) = 1mile(mi) 5280feet(ft) = 1mile(mi)
Thissystemofmeasurementismoredifficulttoworkwithcomparedtothemetricsystembecauseitisnot basedonthenumber10.
Convert741 yardstoinches.
►Solution: 1yd=36in
then741 yd=7
41 #1yd=7
41 36# in=261in
Convert57inchestofeet.
►Solution: 12in=1ft
then57inches 57 4ft ft ft121
1257
43#= = =
Convert38fttoyards.
►Solution: 3ft=1yd
then38feet 38 yd yd31
338 12
32#= = = yds
Example 1
Example 2
Example 3
Imperial Systems1.2
♦ 10Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Convert17160feettomiles.
►Solution: 5280ft=1mi
then17160 17160 3.25ft mi mi mi52801
528017160#= = =
Convert143 milesto:
a)yardsb)feetc)inches
►Solution: a) 1mi=1760yds
then143 mi= 1
43 1# mi=1
43 1760# yds=3080yds
b) 1yd=3ft
then3080yds=3080#1yd=3080#3ft=9240ft
c) 1ft=12in
then9240ft=9240#1ft=9240#12in=110880in
Convert4inchesto:
a)feetb)yardsc)miles
►Solution: a) 12in=1ft
then4inches 4 1 4in ft121
31# #= = = ft
b) 36in=1yd
then in yd4 1 4 1 136 9
# #= = = yd
c) 5280ft=1mile,12in=1ft
therefore1mile 5280 12 63 360in#= = in
then4inches in mi4 1 4 1 163 360 15 840
# #= = = mi
Example 4
Example 5
Example 6
♦ 11Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.2 Exercise Set
1. Findtheequivalentmeasurement.
a) 1yd=ft b) 1ft=yd
c) 1ft= in d) 1in=ft
e) 1yd=in f) 1in=yd
g) 1mi=yd h) 1yd=mi
i) 1mi=ft j) 1ft=mi
♦ 12Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
2. Findtheequivalentmeasurement.
a) 28ft=yd b) 96in=ft
c) 4mi=yd d) 10560ft=mi
e) 9ft=in f) 3mi=ft
g) 5yd=in h) 24yd=ft
i) 432in=yd j) 12320yd=mi
♦ 12Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
3. Findtheequivalentmeasurement.Leaveyouranswerinfractionalform.
a) 10ft=yd b) 66in=ft
c) 3960yd=mi d) 120in=yd
e) 9240ft=mi f) 17ft=yd
g) 26in=ft h) 3696yd=mi
i) 135in=yd j) 9504ft=mi
♦ 13Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. Findtheequivalentmeasurement.Whennecessary,expressyouranswerasadecimaltothenearesthundredth.
a) 8500ft=mi b) 45in=ft
c) 8.25ft=yd d) 1.4yd=in
e) 2323yd=mi f) 3.42mi=ft
g) 451 ft=in h) 19
32 yd=ft
i) 2743 in=yd j) 1.7mi=yd
♦ 13Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
5. Writetheequivalentvalue.
Inches Feet Yards Miles
1
5632
4752
44352
2.4
2816
8712
85536
6. ThedeepestpartofouroceansistheMarianaTrench 7. Themarathonraceis26miles,385yardsinlength. at11947yardsdeep.Howmanymilesdeepisthe Howmanyfeetlongisthemarathon? trench?
♦ 14Lambrick Park Secondary
Section 1.2 - Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
8. Arectangularwindowis5feet3inchesinlength, 9. JanZeleznyoftheCzechRepublicsettheworld and3feet6inchesinwidth.Iftheperimeterofthe recordinthejavelinthrowat107yards,2feet, windowmusthavecaulkingthatcosts32¢perinch, 11inchesonMay25,1996.Howmanyincheswas howmuchwillthecaulkingcost? histhrow?
10. Thefloorofahousemeasures12feet,9inchesby 11. Aswimmingpoolis50ftlong,22ftwide,and 17feet,4inches.Whatwillitcosttocarpetthe averages6ftdeep.Howmanycubicyardsof floorifcarpetcosts$27.00persquareyard? waterwillithold? (Assumenowaste.)
♦ 14Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Ifyoustudyfieldssuchasengineering,chemistryornursing,youwillneedtoconvertmeasurementsbetween thetwosystems.Toconvertbetweenmetricandimperialmeasures,itishelpfultohaveequivalentvalues. Herearesomecommonconversionfactors.
MetrictoImperial ImperialtoMetric1kilometre≈0.621miles1metre≈1.094yards1metre≈3.280feet1centimetre≈0.394inches
1mile≈1.609kilometres1yard≈0.914metres1foot≈0.305metres1inch=2.54centimetres
Comparison Size
(Scale10:1)
Ayardisslightlysmallerthanametre.
(Scale160934:1)
Akilometreisslightlymorethanhalfamile.
(Scale1:1)
Aninchismorethantwiceacentimetre.
1mile
1kilometre
1inch
1centimetre
1metre
1yard
Converting Metric and Imperial Systems1.3
♦ 15Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Findthemissinglengths.
a) 6m=yds
b) 6yds=m
c) 3km=ft
d) 4mi=cm
e) 25cm=mi
►Solution: a) 1m=1.094yds
then6m=6#1m=6#1.094yds=6.564yds
b) 1yd=0.914m
then6yds=6#1yd=6#0.914m=5.484m
c) 1m=3.280ft
then3km=3000m=3000#1m=3000#3.280ft=9840ft
d) 1mi=1.609km,1km=1000m,1m=100cm
then4mi=4#1mi=4#1.609km=6.436km
and6.436km=6.436#1km=6.436#1000m=6436m
and6436m=6436#1m=6436#100cm=643600cm
e) 1cm=0.01m,1m=0.001km,1km=0.621mi
then25cm=25#1cm=25#0.01m=0.25m
and0.25m=0.25#1m=0.25#0.001km=0.00025km
and0.00025km=0.00025#1km=0.00025#0.621mi=0.000155mi
Example 1
♦ 16Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.3 Exercise Set
1. ConvertfromMetrictoImperial.(Answerstothreedecimalplaces.)
a) 1km=mi b) 1m=yd
c) 1m=ft d) 1cm=in
e) 0.621km=mi f) 27.3m=yd
g) 19.8m=ft h) 47.9cm=in
i) 3.7km=yd j) 63m=in
♦ 17Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
2. ConvertfromImperialtoMetric.(Answerstothreedecimalplaces.)
a) 1mi=km b) 1yd=km
c) 1ft=m d) 1in=cm
e) 0.621mi=km f) 27.3yd=m
g) 19.8ft=m h) 47.9in=cm
i) 3.7yd=km j) 63in=m
♦ 17Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
3. Findtheequivalentmeasurement.(Answerstothreedecimalplaces.)
a) 110yds=m (ThelengthofaCanadianfootballfield.)
b) 30cm=in (Thelengthofaruler.)
c) 533km=mi (ThedistancefromEdmontontoSaskatoon.)
d) 6ft,1in=m (Theheightofthisauthor.)
e) 70mi/hr=km/hr (ThespeedlimitontheInterstateHighwayintheUnitedStates.)
f) 110km/hr=mi/hr (ThespeedlimitonsectionsoftheTransCanadaHighway.)
g) 1253mi=km (ThedistancefromVancouvertoLosAngeles.)
♦ 18Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
3. h) 50km/hr=mi/hr (Thespeedlimitonmostcitystreets.)
i) 6ft,3in=m (TheheightofbasketballplayerSteveNash.)
j) 6.5mm=in (Thethicknessofapencil.)
k) 1815.4ft=km (TheheightoftheCNtowerinToronto.)
l) 94.51millionmiles=millionkm (ThedistancefromtheEarthtotheSun.)
m) 261millionkm=millionmiles (ThemaximumdistancebetweenEarthandVenus.)
♦ 18Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. Completethetable.
Object mm ft yd cm in mThicknessofhardwoodfloor 19
Heightofaroom 9
Widthofafootballfield 55
Lengthofapencil 18
Heightofatable 29
Ahomeruninbaseball 135
♦ 19Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
5. Findthemissinglengths.
a) 25squaremetres=squareyards b) 40squarefeet=squaremetres
c) 75squareinches=squarecentimetres d) 5squaremetres=squareinches
e) 8cubicmetres=cubicyards f) 75cubicfeet=cubicmetres
g) 40cubicinches=cubiccentimetres h) 250cubiccentimetres=cubicinches
♦ 19Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
6. ThespeedlimitonB.C.highwaysis110km/hr. 7. Ascalemodelofthefishingschooner,theBluenose, Johnistravellingat70mi/hr.IsJohnspeeding? is20cmlong.Every3centimetresonthemodel represents8yardsontheBluenose.Howmany metreslongistheBluenose?
8. Amaphasascaleshowing2inchesrepresents 9. Oneofthemostanticipatedrecordsintrackand 9kilometres.Howmanymilesapartarecities fieldwasbreakingthe4minutemile.Ifarunner thatare11.3inchesapartonthemap? ranthe1500metreraceatthesameaveragespeed, whattimewouldhetake,tothenearestsecond?
10. Countingtheendzones,aCanadianfootballfield 11. Ametrictonisthemassof1m³ofwater.How measures160yards#55yards.Howmanysquare manycubicfeetis1m³? metresisthisfield?
♦ 20Lambrick Park Secondary
Section 1.3 - Converting Metric and Imperial Systems
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
12. Mikeisrunningat7.5milesperhour.Howmany 13.Marcusisskatingat20m/s.Whatishisspeedin metrespersecondisherunningat? mi/hr?
14. Theknotisaunitofspeedequaltoonenautical 15.Oneknotishowmanym/s? mileperhour,approximately1.151mi/hr.What isaknotinkm/hr?
♦ 20Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Prismsarenamedaccordingtotheshapeoftheirbases.
Thefourprismsshownarerightprismsbecausethelateral(vertical)edgesareperpendiculartotheplaneof thebaseandthetop.
Ifthebaseisaregularpolygon(allsidesequal)thenthecorrespondingprismiscalledaregularprism.
Surface Area of Prisms
Thesurfaceareaofprismisthesumoftheareasofallthefaces,orsurfaces,thatenclosetheprism.
Cube
SurfaceArea= l l l6 6 2# # =^ h
RectangularPrism
SurfaceArea= lw lh wh2 2 2+ +
TriangularPrism
SurfaceArea=2 ab ac bc cd21
+ + +` j
= ab ac bc cd+ + +
whered a b2 2= +
Surface Area and Volume of Prisms1.4
Cube RectangularPrism HexagonalPrismTriangularPrism
l l
l
l w
h
♦ 21
a b
cd
Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Findthesurfacearea.
a)
b)
c)
►Solution: a) SurfaceArea= l6 2#
=6 3 54 cm2 2# =
b) SurfaceArea= lw lh wh2 2 2+ +
=2 6 3 2 6 4 2 4 3# # # # # #+ +
=36 48 24+ +
=108 cm2
c) 5 12x 1692 2 2= + =
x 169 13= =
SurfaceArea=ab ac bc cd+ + +
=5 12 5 4 12 4 13 4# # # #+ + +
=60 20 48 52+ + +
=180 in2
Note: When the units of length are: mm, cm, m, etc., the units of area are: mm², cm², m², etc.
Example 1
3cm 3cm
3cm
3cm
4cm
6cm
5in 12in
4inxin
♦ 22Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Volume of Prisms
Volumeisthemeasureoftheamountofspacecontainedinasolid.
Whiletheformulausedforfindingthesurfaceareaofaprismdiffersdependingontheshapeoftheprism,the formulausedtocomputethevolumeofaprismisthesameforallshapesofprisms.
Volume of a Prism
IfBistheareaofthebaseoftheprism,andhistheheightoftheprism,then:Volume=B h#
Cube
Areaofbase=l l l2# =
Height=l Volume=B h l l l2 3# #= =
RectangularPrism
Areaofbase=l w# Height=h Volume=B h l w h# # #=
TriangularPrism
Areaofbase= ab21
Height=h
Volume=B h ab h21
# #=
TrapezoidPrism
Areaofbase= a b c21+^ h
Height=h
Volume=B h a b ch21
# = +^ h
l l
l
l w
h
a b
hd
a
b h
c
♦ 23Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Findthevolume.
a) b)
c) d)
►Solution: a) Volume=l3
=23
=8 m3
b) Volume=l w h# #
=10 5 3# #
=150 ft3
c) Volume= ab h21#
=21 3 2 4# # #
=12 mm3
d) Volume=Areaofatrapezoid h#
=213 5 10 12$ #+^ h
=270 m3
Note: When the units of length are: mm, cm, m, etc., the units of volume are: mm³, cm³, m³, etc.
Example 2
2m 2m
2m
4mm
3mm
2mm
5ft
3ft
10ft
10m12m
5m
3m
♦ 24Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.4 Exercise Set
1. Determinethesurfaceareaandvolumeoftherightprism.
a) b)
S.A.= S.A.=
V = V =
c) d)
S.A.= S.A.=
V = V =
5ft 5ft
5ft
5cm
4cm
10cm
8mm
6mm10mm
3mm
20m 9m5m
13m12m
10m
15m
♦ 25Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1. e) f)
S.A.= S.A.=
V = V =
g) h)
S.A.= S.A.=
V = V =
10yds20yds
7yds
20ft30ft
8ft
6ft
6cm
8cm
8m12m
♦ 26Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1. i) j)
S.A.= S.A.=
V = V =
k) l)
S.A.= S.A.=
V = V =
8m 12m
5m
4m
3m
8m
9m7m
7m
4mm
3mm5mm
2mm
5ft
6ft12ft
4ft
♦ 27Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
2. AnOlympicsizeswimmingpoolis50mlong,21m 3. Thedimensionsfora wideand2mdeep.Howmanylitresofwaterare barnareshown.What neededtofillthepool?(1m³=1000l) isitsvolume?
4. Abedroomhaslength4.8m,width4.2mand 5. Ifastackof500sheetsofpapermeasures height2.2m. 21.59cm#27.94cm#5cm
a) Findthesurfaceareaofthewallsandceiling. a) Whatisthethicknessofeachsheetofpaper?
b) Ifonelitreofpaintcovers8m²,andMary b) Whatisthevolumeofonesheetofpaper? appliestwocoatsofpaint,howmanylitresof paintwillsheneedforthisroom?
10m3m
10m6m
2m
♦ 28Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
6. Thedimensionsfora 7. Asectionoffreeway1kmlongand15mwideisto sandboxareshown. beresurfacedwith25cmofasphalt.Whatisthe Ifthewallsofthe volumeofasphaltneeded,incubicmetres? sandboxaretobe paintedinsideandoutside, whatisthetotalareatobe painted?
8. Thelengthofarectangularsolidisthreetimesthe 9. Apieceofcheeseisin widthandtheheightistwicethewidth.Ifthe theshapeofaright volumeis162cm³,whatisthewidthofthe triangularprismofthe rectangularsolid? givendimensions. Whatisthevolumeof thepieceofcheese?
3m2.5m
0.6m
6cm 8cm
5cm
♦ 29Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
10. Acubehasavolumeof27cm³.Whatisits 11. Trishaboughta40litrefishtank.Shewastoldthat surfacearea? afishtankcouldsupportonegoldfishforevery 2500cm³ofwater.Howmanygoldfishcanthe tanksupport?(1litre=1000cm³)
12. Arockissubmergedinarectangularprismwhose 13. Thebaseofarighttriangularprismhassidesof basemeasures10cmby15cm.Ifthewaterlevel 3,4,5cm.Thevolumeoftheprismis84cm³. risesfromaheightof8cmto11cm,whatisthe Findtheheightoftheprism. volumeoftherock?
♦ 29Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
14. Thedimensionsfora 15. Findthe swimmingpoolin volumeof theshapeofa thebarn. prismareshown. Howmanylitresof waterdoesittaketofill thepool?(1000litres=1m³)
16. Adrainagecanalisaright 17. Thevolumeofanopen-toppedboxwitha trapezoidprismofthe squarebaseis32cm³.Ifitsheightis2cm, indicateddimensions. whatisthesurfaceareaofthebox? Whatisthevolume oftheprism? 13m
10m
50m
20m
16 m
32 m 6 m4 m6m
5m
4m
10m
1m
♦ 30Lambrick Park Secondary
Section 1.4 - Surface Area and Volume of Prisms
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
18. Aregularhexagonalbasedprismhassidesof4cm 19. Arightprismwhosebaseisarhombushas andaheightof5cm. diagonalsof12cmand16cm,withaheightof6cm.
a) Whatisthesurfaceareaoftheprism? a) Whatisthesurfaceareaoftheprism?
b) Whatisthevolumeoftheprism? b) Whatisthevolumeoftheprism?
20. Findthesurfacearea 21. Findthevolumeofarighttriangularprismwith oftheprism. height x2 1+^ h.Thebaseisanisoscelesright trianglewithahypotenuseof x2 .x
x
2x
2x
4x
♦ 31Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Surface Area of a Pyramid
Apyramidisasolidfigure,whoselateralfacesaretrianglesthathaveonepointincommon.
Thisiscalledasquarepyramidbecauseitsbaseissquare.Determiningthesurfaceareaofthispyramid requiresfindingtheareaofthebase,plustheareaofthefourlateralfaces.
Determinethesurfaceareaofthesquarepyramid.
►Solution: Ifthedistancefromthecentreofthebasetotheedgeis5,thenthelengthandwidthofthe baseis10.
Areaofbase=10 10 100# = cm²
Tofindtheslantheight,usethePythagoraeantheorem.
5 12s 1692 2 2= + =
s 13= cm
Areaofonelateralface=21 10 13 65# =^ h cm²
Thereforethesurfacearea= ( )100 4 65 360+ = cm²
Example 1
Surface Area and Volume of Pyramids1.5
PerpendicularHeight(h)
SlantHeight(s)
LateralEdge
Base(B)
LateralFace
SlantHeight(s)
5cm
10cm
12cm
♦ 32Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Volume of a Pyramid
Consideracubeoflength2x.Drawthefourdiagonalsofthecube.Theareaofthebaseofeachpyramidis x x x2 2 2 2=^ ^ ^h h h .Thepyramidswillmeetatthecentreofthecubewithheightxfromthebase.Ifyoulook carefully,youwillseesixequalsquarebasedpyramids,onefromeachofthesixsidesofthecube.
LetthevolumeofeachsquarebasepyramidbeV.Thenthevolumeofthecubeis6V.
So V x6 2 3= ^ h ,thereforeV x x x x x
61 2
61 2 2
31 23 2 2
= = =^ ^ ^ ^ ^h h h h h
WecansaythevolumeofeachpyramidisV=31 #(areaofbase)#(height).Thisformulaistrueforall
pyramids.
Volume of a Pyramid
ThevolumeofanypyramidwithareaofbaseB,andheighthisV B h31#= ^ h
Calculatethevolumeoftherectangularpyramid.
►Solution: V B h31#= ^ h
31 6 8 10#= ^ ^h h
160 in3=
Example 2
2x
x
2x
2x
8in6in
10in
♦ 33Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Usingthenet,determinethevolumeofthesquarebasedpyramid.
►Solution: Solvefortheheightofpyramid,h.
h 5 132 2 2+ =
169 25h 1442= - =
h 12= cm
V B h31#= ^ h
31 10 10 12#= ^ ^h h
400 cm3=
Thevolumeofarectangularpyramidis54cm³.Determinethedimensionsofitsbase,ifthe lengthofthebaseistwicethewidth,andtheheightisthreetimesthewidth.
►Solution: V = B h31 #^ h
54= x x x31 2 3#^ ^h h
54= x2 3
27= x3
x = 3
Thereforethebaseis3cm# 6cm.
5cm
13cm h
Example 3
Example 4
10cm
13cm
♦ 34Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.5 Exercise Set
1. Findthetotallateralarea(notincludingthebase)ofeachregularpyramid.
a) Triangularbasewithsides5cmandslantheight b) Squarebasewithsides5cmandslantheight8cm. 8cm.
c) Pentagonalbasewithsides5cmandslantheight d) Hexagonalbasewithsides5cmandslantheight 8cm. 8cm.
e) Octagonalbasewithsides2cmandslantheight f) Decagonalbase(10sides)withsides2cmand 8cm. slantheight8cm.
g) Dodecagonalbase(12sides)withsides2cm h) Hexadecagonalbase(16sides)withsides2cm andslantheight8cm. andslantheight8cm.
♦ 35Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
2. Findthevolumeofeachpyramid.
a) Areaofbaseis15m²andheightis5m. b) Areaofbaseis18.6in²andheightis7in.
c) Areaofbaseis270ft²andheightis8yds. d) Areaofbaseis36m²andheightis200cm.
e) Areaofbaseis97.2cm²andheightis86mm. f) Areaofbaseis1200in²andheightis 43 ofayard.
g) Areaofbaseis3m²andheightis340mm. h) Areaofbaseis9m²andheightis2ft.
♦ 36Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
3. Findthesurfaceareaandvolume.
a) b)
S.A.= S.A.=
V = V =
c) d)
S.A.= S.A.=
V = V =
6cm6cm
4cm
10cm10cm
12cm
16m16m
17m 7m
Alledgesare10m
♦ 37Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. Whatistheratioofthe 5. Findthesurfaceareaof volumeofthepyramid pyramidABCDEinscribed tothevolumeofthe insideacube. rectangularsolid?
6. Twopyramidsareinscribedincubes. 7. Aregularhexagonalpyramidhasbaseedgesof length1cm,andlateraledgesoflength2cm. i) ii)
a) Whichpyramidhasthegreatestvolume? a) Whatisthevolumeofthepyramid?
b) Whichpyramidhasthegreatestsurfacearea? b) Whatisthesurfaceareaofthepyramid?
A
B
E
C
D
♦ 38Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
8. Arightrectangularpyramidhasabase6cmby 9. Findthelateralsurfaceareaofasquarepyramid 8cm,andaheightof10cm.Whatisthevolume whoseheightis8cmandwhosebaseonedgeis ofthepyramid? 12cm.
10. Thebaseofaregulartriangularpyramidisan 11. Astonemonumentistheshapeofapyramid. equilateraltriangle.Thevolumeofthepyramid Theareaofthebaseis81m²andtheheightofthe is27cm³andtheheightis3 3 cm.Whatisthe monumentis10m.Thestoneweighsabout lengthofthesideofthebase? 3000kg/m³.Howmanytonnesdoesthemonument weigh?(2000kg=1metrictonne)
♦ 39Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
12. Findthesurfaceareaandvolumeofaregular 13.Analtitudeofasquarepyramidis10cm,andthe hexagonalpyramidwithbaseedge14inches sidesofthebaseare15cm.Findtheareaofa andheight24inches. crosssectionatadistanceof4cmfromthetop ofthepyramid.
14. Ifyoudoubleallthedimensionsofapyramid,what 15. Apyramidhasarighttriangularbaseanda doesitdotothesurfacearea?Volume? volumeof120m³.Theshortersidesofthebase are6mand9mlong.Findtheheightofthe pyramid.
♦ 39Lambrick Park Secondary
Section 1.5 - Surface Area and Volume of Pyramids
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
16. Findthetotalsurfaceareaofaregularpyramid 17. Apyramidhasarectangularbasewithlengthtwice whoseheightis15cmandwhosebaseisasquare thewidth.Iftheheightis6cmandthevolumeis withsides16cm. 256cm³,whatarethedimensionsoftherectangular base?
18. Findthetotalsurfaceareaofaregularpyramid 19. Ifthediagonalsofacubearedrawn,theymeetat whoseheightis3cm,andwhosebaseisarectangle thecentreofthecube.Whenthediagonalsare withsides6cmand8cm. drawn,howmanypyramidsareformed?Ifthe edgeofthecubeis9cm,findthevolumeofone ofthepyramids.
♦ 40Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Cylinders
Acylindercanbethoughtofasarectangularprismwithacircularbase.Forthatreason,calculatingthesurface areaandvolumeisverysimilartohowitisdoneforaprism.
SurfaceArea= Areaoftopandbottomfaces + Areaoflateralside = 2 r2r + rh2r
Volume = Areaofbase # height = r2r # h
Surface Area and Volume of a Cylinder
SurfaceArea= r rh2 22r r+
Volume= r h2r
Determinethesurfaceareaandvolumeofacylinderwithradius4cmandheight6cm.
►Solution: SurfaceArea= r rh2 22r r+
=2 4 2 4 62# # #r r+
=80 251.3 cmcm2 2-r
Volume = r h2r = 4 62# #r
= cm . cm96 301 63 3-r
Note: The answer “80 cm2r ” is accurate, “251.3 cm2” is rounded to one decimal place.
r
h
r
h
Example 1
Surface Area and Volume of Cylinders, Cones, and Spheres1.6
♦ 41Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Cones
Aconecanbethoughtofasapyramidwithacircularbase.Forthatreason,calculatingthesurfaceareaand volumeisagainverysimilartohowitisdoneforapyramid.
(l=slantheight,withl r h2 2 2= + )
SurfaceArea = Areaoflateralside + Areaofbase = rlr + r2r
Volume=31 # Areaofbase # height
=31 # r2r # h
Surface Area and Volume of a Cone
SurfaceArea= rl r2r r+ ,withl r h2 2 2= +
Volume= r h31 2r
Determinethesurfaceareaandvolumeofaconewithradius5ftandheight12ft.
►Solution: Ifr=5ftandh=12ft,thenl r h l5 12 169 132 2 2 2 2"= + = + = = ft
SurfaceArea= rl r2r r+
= 5 13 52# # #r r+
= 90 ft2r
Volume = r h2r = 5 122# #r
= 300 ft3r
Example 2
LateralSide Baser
h r
l
l+
♦ 42Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Spheres
Aspheremaybethoughtofasallpointsinspacethatareafixed,orequaldistancefromagivenpoint.The givenpointisitscentre,andthedistance(r)istheradiusofthesphere.Halfofasphereiscalledahemisphere.
Toprovetheformulasforthesurfaceareaandvolumeofasphererequirestheuseofcalculus.Soherewe simplygivethemtoyou.
Surface Area and Volume of a Sphere
SurfaceArea= r4 2r
Volume= r34 3r
Determinethesurfaceareaandvolumeofaspherewithradius6mm.
►Solution: SurfaceArea= r4 2r
=4 62# #r =144 mm 2r
Volume= r34 3r
=34 63# #r
= mm288 3r
Determinethesurfaceareaandvolumeofahemispherewithcircumference8r cm.
►Solution: C r r2 8 4"r r= = =
SurfaceArea r r2 2 2r r= + Volume r332 r=
r3 2r= 2 3
32 r= ^ h
3 4 2r= ^ h 316 r= cm³
48r= cm²
Example 3
r
Example 4
♦ 43Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1.6 Exercise Set
1. Determinethesurfaceareaandvolume.
a) b)
S.A.= S.A.=
V = V =
c) d)
S.A.= S.A.=
V = V =
4m
8m6mm
10mm
1.5mm
3cm
2cm
4cm
3cm
5m3m
8m
♦ 44Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1. e) f)
S.A.= S.A.=
V = V =
g) h)
S.A.= S.A.=
V = V =
8cm
3cm
3cm
12cm
4cm
9cm
4cm9cm
5m
18m
♦ 45Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
1. i) j)
S.A.= S.A.=
V = V =
2. Agreenhouseissemi- 3. Soupissoldintwocansizes.Thecanis cylindricalinshape.If cylindricalinshape.TheheightofcanAistwice clearvinylisusedto theheightofcanB.TheradiusofcanBistwice coverthegreenhouse, theradiusofcanA.CanBcoststwiceasmuch howmuchmaterialis ascanA.Whichcanisthebetterbuy? neededif10%extrais requiredforwaste?
5cm 10ft
4m10m
♦ 46Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. Acertaintypeofdrainagetileismadefromclay. 5. IfrectangleABCDis Eachtileisacylindricalshell30cmlongwithan isrevolvedaboutthe insideandoutsidediameterof10cmand12cm. lineAD,whatisthe Whatisthevolumeofeachclaytile? volumeofthespace throughwhichitmoves?
6. Asteelpipehasaninsideradiusof4cmand 7. Apapercupistheshapeofaconewithradius3cm anoutsideradiusof5cm.Calculatethevolume andheight4cm.Howmuchpaperisneededto ofsteelina2.5mlengthofpipe. makethiscup?
2m
4mA
B
D
C
♦ 47Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
8. Acylinderhasavolumeof320πcm³anda 9. Supposetheradiusandheightofacylinderare heightof5cm.Findtheradiusofthecylinder. bothdoubled.Byhowmuchisthesurfacearea increased?Byhowmuchisthevolumeincreased?
10. Acylinderofradius6cmandheight18cmisfull 11. Calculatethevolumeofthe ofwater.Whatmustbetheheightofaconewith solidformedbyrotatingthe radius9cmtoholdthesameamountofwater? figurearoundthelineAB.
2cm
3cm
A
B
C
♦ 47Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
12. Twowaterpipesofthesamelengthhavearadius 13. Calculatetheheightofarightcircularconewhose of3cmand4cm.Ifthesetwopipesarereplaced volumeis75π,andwhosebasehasadiameterof byonepipeofthesamelength,whatmustbethe 10ft. radiusofthenewpipeifthevolumeisthesame?
14. Whatisthelateralsurfaceareaofarightcircular 15. Thediameterandheightofarightcircularconeare coneofheight12inandradius5in? thesame.Ifthevolumeoftheconeis144πcm³, whatistheradiusofthecone?
♦ 48Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
16. Iftheradiusofarightcircularcylinderis3cm, 17. Acylindricalblockofcheese andthetotalsurfaceareais42πcm²,whatisthe hasa60°sliceremoved.Ifthe height? volumeoftheremovedsliceis 18πcm³,whatistheheightof theblockofcheese?
18. Arightcylinderhasheight8mmand 19. Acanofpeashasaheightof15cmanda circumference6πmm.Whatisthevolume circumferenceof10πcm.Whatistheamountof ofthecylinder? paperneededforthelabelonthecanofpeas?
6cm
♦ 48Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
20. Thetotalsurfaceareaofarightcircularconeis 21. Asphericalmetalshellis1cmthick.Iftheoutside 90πcm².Itsradiusis5cm.Whatisthevolume diameteris8cm,findthevolumeofmetalinthe ofthecone? shell.
22. Asiloiscomposedofa 23. Ahemispherehasa hemisphereontopofa diameterof10cm. cylinder.Ifthecylinder Whatisthetotal heightanddiameterare surfaceareaofthe both8m,whatisthe hemisphere? volumeofthesilo?
10cm8m
8m
♦ 49Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
24. Ahemisphericalroom 25. Ifasphereandaconehavethesameradiusand requiresfourcansof volume,whatmustbetheheightoftheconein painttopaintthefloor. termsoftheradius? Howmanycansof paintarerequiredto paintthewalls?
26. Aspherewitharadiusof4cmhasa45°section 27. Aspherewitharadiusof4cmhasa45°section removed.Whatistheremainingvolumeofthe removed.Whatistheremainingsurfaceareaof sphere? thesphere?
♦ 50Lambrick Park Secondary
Section 1.6 - Surface Area and Volume of Cylinders, Cones, and Spheres
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
28. Aspherefitsexactlyinto 29. Asphereofradiusrisinscribed acube.Whatistheratio inaconewithdiameter ofthesurfaceareaofthe AC=AB=BC.Findthe spheretothesurfacearea ratioofthevolumeofthe ofthecube? spheretothevolumeof thecone.
30. Threetennisballsarepackedtightlyindifferentcontainers. Whatistheratioofthevolumeofthetennisballstothe volumeoftheboxinfiguresa,bandc?
a) b) c)
A
B
C
r
♦ 51Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.1
1. Add.
a) 4.6m+25cm+240mm=mm=cm=m
b) 1.2km+612m62583cm=km=m=cm
c) 0.0075km+0.32m+61.3cm=km=m=cm
d) 0.25km+6200cm+12000mm=m=cm=mm
Chapter Review1.7
♦ 52Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.2
2. Add.
a) 0.5mi+438yd+812ft=mi=yd=ft
b) 720in+96ft+51yd=in=ft=yd
c) 0.2mi+32yd+78ft=mi=yd=ft
d) 0.25mi+360yd+6600in=mi=yd=ft
♦ 52Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.3
3. ConvertfromMetrictoImperialunits.(Answerstothreedecimalplaces.)
a) 5.3km=mi b) 63cm=in
c) 345mm=in d) 82m=ft
e) 0.28km=yd f) 74m=yd
g) 436cm=ft h) 428000mm=mi
♦ 53Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
4. ConvertfromImperialtoMetricunits.(Answerstothreedecimalplaces.)
a) 5.3mi=km b) 63in=cm
c) 345in=mm d) 82ft=m
e) 280yd=km f) 74yd=m
g) 4.36ft=cm h) 0.0428mi=mm
♦ 53Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.4
5. Determinethesurfaceareaandvolumeoftherightprisms.
a) b)
S.A.= S.A.=
V = V =
c) d)
S.A.= S.A.=
V = V =
12cm
9cm15cm
4cm 6in9in
8m 12m5m
3m
5ft
7ft
♦ 54Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.5
6. Determinethesurfaceareaandvolumeofthepyramids.
a) b)
S.A.= S.A.=
V = V =
12in12in
8in
14cm14cm
24cm
♦ 55Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
7. Apyramidandaprismbothhavethesamebaseand 8. Apyramidhasarighttriangularbasewithsides height.Determinetheratioofthevolumes. 5cm,12cmand13cmlong.Determinetheheight ofthepyramidifthevolumeis120cm³.
9. Twopyramidsaresimilar.Thevolumeofthelarger 10. Twopyramidsaresimilar.Thevolumeofthelarger pyramidis500cm²andtheratioofthebaseareasof pyramidis500cm²andtheratioofthebaseareasof thepyramidsis9to25.Whatistheratioofthe thepyramidsis9to25.Whatisthevolumeofthe heightsofthepyramids? ofthesmallerpyramid?
♦ 55Lambrick Park Secondary
Section 1.7 - Chapter Review
Copyright © 2009 by Crescent Beach Publishing. No part of this publication may be reproduced without written permission from the publisher.
Section 1.6
11. Determinethesurfaceareaandvolumeofthesolids.
a) b)
S.A.= S.A.=
V = V =
c) d)
S.A.= S.A.=
V = V =
4ft
6in
12in
8in
9in
6mm10mm
♦ 56
2cm
1cm
3cm
2cm
Lambrick Park Secondary
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