可汗学院数学题目34Volumewordprobs.docx

可汗学院数学题目34Volumewordprobs.docx

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可汗学院数学题目34Volumewordprobs

Volumewordproblems

1.

Camismakingapartyhat,shownatleft,intheshapeofaconeforhisbirthday.Thecircumferenceofthepartofhisheadwherethehatwillrestis56centimeters（cm）.Iftheheightofthehatis25cm,whatisthevolumeofCam'shat,measuredincubiccentimeters（cm3）?

Useπ≈3.14.

A.233cm3

B.2,081cm3

C.16,354cm3

D.20,515cm3

Correctanswer:

BDifficultylevel:

2

2.

Asetof3cylindricalcanistersallhavediameter8centimeters（cm）.Theheightsofthecanistersare16cm,12cm,and9cm,respectively.Whatistheapproximatetotalvolumeofthe3canistersincubiccentimeters（cm3）?

Useπ≈3.14.

A.804cm3

B.1,055cm3

C.1,859cm3

D.7,436cm3

Correctanswer:

CDifficultylevel:

2

3.

Acakepanisintheshapeofarightrectangularprism20centimeters（cm）longby20cmwideby5cmhigh.Thepancontains1,000cubiccentimeters（cm3）ofbatter.Approximatelyhowfaristhecakebatterfromthetopofthepan?

A.1cm

B.**cm

5cm

C.7cm

Correctanswer:

BDifficultylevel:

2

4.

Ahouseholdaquariumtankintheshapeofarectangularprismhasabaselengthof24inches（in）andabasewidthof15in.Theheightofthewateris12inabovethebase.Duringcleaning,900cubicinchesofwaterisremoved.Whatisthechangeintheheightofthewaterininches?

Correctanswer:

2.5Difficultylevel:

2

5.

Adolfowantstosendhisfriendaposterthatis65centimeters（cm）wideand92cmlong.Hewillmailtheposterinacylindricalcontainerwithavolumeof5,200cubiccentimeters（cm3）.Adolforollsupthepostersothatthewidthoftheposterisalignedwiththeheightofthecontainer.Approximatelywhatisthelargestradiusthecontainercouldhave?

Useπ≈3.14.

A.4cm

B.5cm

C.8cm

D.25cm

Correctanswer:

BDifficultylevel:

2

6.

Adieiscreatedbysmoothingthecornersofaplasticcubeandcarvingindentedpips.Theoriginalcubehadanedgelengthof2centimeters（cm）.Thevolumeofthefinaldieis7.5cm3.Whatisthevolumeofthewastegeneratedbycreatingthediefromthecubeincm3?

Correctanswer:

0.5Difficultylevel:

2

7.

Thevolumeofthetriangularprismshownaboveis160cubiccentimeters（cm3）.Whatistheverticalheight,h,incentimeters（cm）,ofthetriangularbaseoftheprism?

A.5cm

B.8cm

C.12cm

D.40cm

Correctanswer:

BDifficultylevel:

2

8.

Seanhasorderedagiftonlineandwastolditwillbedeliveredinacube-shapedgiftboxwithvolume8,000cubiccentimeters（cm3）,shownatleft.Inordertopurchaseenoughwrappingpapertocoverthebox,hemustcalculateitssurfacearea.Whatisthesurfaceareaofthebox,insquarecentimeters（cm2）?

A.1,200cm2

B.1,600cm2

C.2,000cm2

D.2,400cm2

Correctanswer:

DDifficultylevel:

2

9.

Awoodendoorwedgehastheshapeofarighttriangularprismasshownabove.Therighttriangularfaceshavealengthofl=10centimeters（cm）andaheightofh=4cm.Theprismhasawidthofw=3cm.Whatisthevolumeofthedoorwedgeincubiccentimeters?

Correctanswer:

60Difficultylevel:

2

10.

OneoftheGreatPyramidsofGiza,thepyramidatKhufushownabove,hasasquarebasewithsidesoflength230meters（m）.Theoriginalverticalheightoftherightpyramidisbelievedtohavebeenapproximately146.5m.Duetoerosionoverseveralthousandyears,theheightisnowapproximately139m.Assumethatthepresentfigure,shownatleft,isstillarightpyramidwiththesamebase.Approximatelyhowmuchdidthevolume,measuredincubicmeters（m3）,ofthepyramidatKhufudecreasesinceitwasbuilt?

A.575m3

B.132,250m3

C.2,451,033m3

D.2,583,283m3

Correctanswer:

BDifficultylevel:

2

11.

Acylinderandconehaveequalvolumesandradiiofequallength.Iftheheightoftheconeis24centimeters,thenwhatistheheightofthecylinderincentimeters?

Correctanswer:

8Difficultylevel:

2

12.

Anewdictionaryintheshapeofarectangularprismwillhaveathicknessof3inches（in）.Thevolumeofthedictionarywillbe216in3​.Whatmustbetheareaofthefrontcover,afaceperpendiculartothethickness,insquareinches?

Correctanswer:

72Difficultylevel:

2

13.

Acubeofgoldwithanedgelengthof3inches（in）ismeltedandreformedintoarectangularprismwithawidthof2.5inandaheightof2in.Ifthevolumeisunchangedduringmelting,whatisthelengthoftheprismofgoldininches?

Correctanswer:

5.4Difficultylevel:

2

14.

Atopisformedbyfusingtwoidenticalrightcircularconesbytheirbasesasshownatleft.Theheightofthetop,h,whichisthedistancebetweenthetwoconepoints,is6centimeters（cm）.Thediameterofthecircularconebases,d,isalso6cm.Whatisthevolumeofthetop,incubiccentimeters?

A.9

B.18

C.36

D.72

Correctanswer:

BDifficultylevel:

3

15.

Anyahastwodifferentsizedcylindricalcoffeemugs.Thelargermughasaninternalheightof15centimeters（cm）,andthesmallermughasaninternalheightof10cm.Bothmugshaveaninternaldiameterof8cm.Whichofthefollowingisclosesttothedifferenceincubiccentimeters（cm3）betweentheinternalvolumeofthelargermugandtheinternalvolumeofthesmallermug?

A.63cm3

B.251cm3

C.754cm3

D.1,005cm3

Correctanswer:

BDifficultylevel:

3

16.

Amulti-layercakeisintheshapeofarightcylinder.Theheightofthecakeis20centimeters（cm）,anditsradiusis10cm.Ifeachofthecakelayershasavolumeofapproximately1,250cubiccentimeters,thenhowmanylayersdoesthecakehave?

Correctanswer:

5Difficultylevel:

3

17.

Arectangularprismandcubehaveequalvolumes.Thelengthoftherectangularprismis12centimeters（cm）anditswidthis8cm.Ifeachsideofthecubeis12cm,thenwhatistheheightoftherectangularprismincentimeters?

Correctanswer:

18Difficultylevel:

3

18.

Asoupmanufacturersellsitssoupinrightcylindricalcans.Thecanshaveadiameterof6centimeters（cm）andaheightof10cm.Ifthemanufacturerfillseachcanto90%capacitywithsoup,roundedtothenearestcubiccentimeter,whatistheapproximatevolumeofsoupineachcan?

Correctanswer:

254Difficultylevel:

3

19.

Anarchitecthascreatedascaledrawingforaresidentialtownhouseintheshapeofarectangularprism.Inthedrawing,theinternalwidthofthetownhouseislabeledas18feet（ft）,theinternallengthas20ft,andtheinternalheightas30ft.Thelocalbuildingdepartmenttellsthearchitectthatifbuilt,thebuildingwouldbetootallaccordingtolocalzoninglawsandthatitsheightmustbereducedby10%.Ifthearchitectcreatesasecondscaledrawingwherethetownhouse'sheightisreducedby10%,whatwillbeitsnewproposedinternalvolumeincubicfeet?

Correctanswer:

9720Difficultylevel:

3

20.

Atroughshapedashalfofacircularcylinderisbeingconstructedasshownatleft.Itisabletohold0.5cubicmeters（m3）ofwater.Additionally,itswidth,w,is50centimeters（cm）.Approximatingπas3.14,whatisthelengthofthetrough,l,tothenearesttenthofameter?

A.**

B.**

C.**

**

Correctanswer:

CDifficultylevel:

3

21.

Acylindricalsodacanhasavolumeof108πcubiccentimeters（cm3）andaheightof12cm.Whatisthesurfaceareaofthesodacaninsquarecentimeters?

A.18

B.36

C.72

D.90

Correctanswer:

DDifficultylevel:

3

22.

Theformulaforthesurfaceareaofasphereis:

whereAisthesurfaceareaandristheradius.AsimplifiedmodeloftheEarth'scrustisahollowsphericalshellwithanouterdiameterof8,000miles（mi）andathicknessof10mi.Usingthefactthatthevolumeofashellisapproximatelyequaltoitsoutersurfaceareatimesitsthickness,whatistheapproximatevolumeoftheearth'scrustincubicmilesaccordingtothismodel?

A.64,000,000

B.160,000,000

C.640,000,000

D.2,560,000,000

Correctanswer:

CDifficultylevel:

3

23.

Apaintcanintheshapeofarightcircularcylinder,shownatleft,hasaheightof20centimeters（cm）.Thecircumferenceofthebaseofthecanis43.96cm.Tothenearesttencubiccentimeters（cm3）,whatistheapproximatevolumeofthepaintcan?

A.2,760cm3

B.3,080cm3

C.30,340cm3

D.121,360cm3

Correctanswer:

BDifficultylevel:

3

24.

Aconeandspherehaveequalvolumesandradiiofequallength.Iftheheightoftheconeis36centimeters,thenwhatisthelengthoftheradiusofeachshapeincentimeters?

Correctanswer:

9Difficultylevel:

3

25.

Arighttriangularprismwithanequilateraltriangularbaseisshownabove.Theheightoftherighttriangularprismisequalto7feet（ft）,andeachsideofthetriangularbaseisequalto5ft.Whatisthevolumeoftherighttriangularprism,roundedtothenearestcubicfoot?

Correctanswer:

76Difficultylevel:

3

26.

Arighttriangularprismwitharightisoscelestriangularbaseisshownabove.Theheightoftheprismisequalto9centimeters（cm）,andthebaseoftherightisoscelestriangleisequalto8cm.Whatisthevolumeoftheprism,roundedtothenearestcubiccentimeter?

Correctanswer:

144Difficultylevel:

3

27.

Acylinderandspherehaveequalvolumesandradiiofequallength.Iftheheightofthecylinderis8centimeters,thenwhatisthelengthoftheradiusofeachshapeincentimeters?

Correctanswer:

6Difficultylevel:

3

28.

TheroofthetheEricssonGlobeinStockholmisshapedlikeahemispherewithavolumeof111,000πcubicmeters（m3）.WhatisthediameteroftheroofoftheEricssonGlobeinmeters?

A.

B.

C.

D.

Correctanswer:

DDifficultylevel:

3

29.

Abuildingcontractorhasapickuptruckwitharearstorageareaintheshapeofarectangularprism.Thestorageareahasalengthof80inches（in）,awidthof60in,andaheightof44in.Shewantstofilltheentirestorageareawithequ