Name:
DateDue: AcceleratedGeometry‐Semester2
ProblemSet#11–SurfaceAreaandVolume
Pleasebecarefultodothefollowing:
 Writeeachformulaused.
 Provideadiagramwhenpossible.
 Beclearwhenmakingsubstitutions.
 Allanswersmustbeexactunlessstatedotherwise.
1. ThereisanewowneratChef’sChoiceIceCream.Thenewownerwantstomakeanextralarge
waffleconewithaslantheightof25cmandaheightof20cm.Howmanycubiccentimetersof
icecreamwillfitinthisnewwafflecone.
2. Thesurfaceareaofacertainsoftballisapproximately16πin2.Tothenearesttenth,findthe
volumeofasoftball.
3. Thecircumferenceofasphereis72πmm.Findthesurfaceareaofthesphere.
4. Whichwillholdmore:Acylinderwithheightof14andcircumferenceof3πorahexagonal
prismwithsidelength4andaheightof2?
5.
Whichhaslesssurfacearea:acylinderwithheightof14andcircumferenceof3πorahexagonal
prismwithsidelength4andaheightof2?
6.
Adiehasaheightof2cm.Eachblackdothasaradiusof.2cm.Howmanysquareinchesofthe
dieiscoloredwhite?
7. Findthelateralareaforthefigureshownbelow.
8. Theperimeterofarhombusmeasures52units.Theshorterdiagonalis10units.Finditsarea.
9. Thefigurebelowisaregularpentagonalpyramid.Eachsideofthebasehasalengthof6cm.The
apothemofthepentagonbasehasalengthof4.1cm.Theslantheightofthepyramidis10cm.
Tothenearesttenth,findthedifferenceinthevalueofthelateralareaandtotalsurfaceareaof
thepyramid.
10. Findthevolumeofthistrapezoidalprism:
11. Theapothemofanequilateraltrianglemeasures 5 3 units.Finditsarea.
12. Findtheareaoftheshadedregionbetweenthecircleandtheregularhexagoniftheradiusofthe
circleis8.
13. Acylindricalcorewithadiameterof4unitsistakenoutofandperpendiculartothelateralside
oftheregularhexagonalprismbelow.Findthetotalsurfaceareathatresults.
14. Youarebuyingagazebothatishexagonalinshapewithsidelengthsof10feet.Youarealso
planningonsurroundingthegazebowithacircularcementpatiowiththediameterof22feet.
Calculatetheareathatwillbecoveredincement.
15. IfpointQhascoordinates(4,4,9)andthebaseoftheconeistangenttothex‐andy‐axes,findhe
volumeofthecone.
Q
z
y
x
16. Findtheratioofvolumesofaconeandacylinderthathavethesamebaseandheight.Write
yoursolutionas VCylinder : VCone .
17. Thereisacylindricalbucketwithadiameterof16inchesandaheightof36in.Thebucketis
filledwith10softballswithcircumferenceof12in.Calculatehowmanycubicinchesofempty
spaceisinthebucket.
18. (2pts)LetPbeanypointintheinteriorofrectangleABCD.Fourtrianglesareformedbyjoining
PtoeachvertexA,B,CandD.Showthat A APD  ABPC  A APB  APCD .
A
B
P
D
C
19. (5pts)Youaremaking30chocolatedippedicecreamconestosharewithyourGeometryclass.
Youplanondippingtheentireconeinchocolate.Youwillneedtodothisprocessthreetimesin
ordertoensureeachconeiscoatedproperly.Theconesare8cmhighandhavea6cmradius.
Youhaveenoughconesandicecream,butyouneedtobuythechocolate.Ifa10,000cubiccm.
canofchocolatecosts$3.25,howmuchwillyouspendonchocolate(include7%salestax).Also,
howmuchicecreamwilleachpersongetifyoubasetheicecreamonthepicturebelow(youwill
filltheentireconewithicecreamaswell).
20. (5ts)Youarebuildingadoghouseoutofwood.Belowisthelayoutofthedoghouse.The
openingforthedogtoenterwillbeasemicirclewithadiameterof24inches.Calculatethetotal
costofthedoghouseconsideringthefollowing:
 Youdecidetousewood:2x4’sthataresoldfor$1.24/linearfoot.Forthe
entryway,youwillbind2x4’stogether,thenmitersawtheexcess.
 Youdecidetopaint:MidnightBlueissoldat12.45/gallon.Eachgalloncovers500
squarefeet.
 Youwillneednails,woodglue,androofbracketsupports:Suppliesareestimated
at$27.50
 Youdecideonawaterproofoutdoorcushionforwhenyourdogfallsasleep
outside:Theoneyouloveis$34.99.
63 in
Sides:
24 in
24 in
54 in
49 in
Roof:
63 in
Left of
Roof
67 in
49 in
Front of
15 in Roof 24 in
Right of
Roof
67 in
Back of
15 in Roof 24 in