chapter 11 circumference, area, and volume 11.1 ... ideas ch...11.8 surface areas and volumes of...
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BigIdeasCh11Notes
Geometry Name___________________________________________ Date____________________________Period__________
Chapter11Circumference,Area,andVolume
11.1CircumferenceandArcLength
Circumferenceis______________________________________________________________________
Increasethenumberofsidesofacircumscribedpolygon.
Thera@oof_________________________________over__________________________approaches___________________.
� _______________________
FormulafortheCircumference: C=ArcLengthisapor@onofthe_______________________________.
Arclength=
Cd=
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BigIdeasCh11Notes
UsingCircumference
TheUnitCircleis________________________________________________________________
ArcLengthof� =
ArcLengthof� =
Radians
Radiansis________________________________________________________________
Circumferenceofaunitcircle=_______________radians.
Conver@ngfromdegreestoradians:
Conver@ngfromradianstodegrees:
a)Convert45˚toradians b)Convert� radianstodegrees
c)Calculatethearclengthonacirclewithradiusof5metersandarcangleof� radians.
11.2AreasofCirclesandSectorsAreaofaCircle=
Example:Aregionwitha3-mileradiushasapopula@ondensityofabout6195peoplepersquaremile.Findthenumberofpeoplewholiveintheregion.
ASectoris___________________________________________________________________________________
AreaofaSector=
Example:Findtheareaofthesectorsformedby� .
CD!
AB!
3π2
2π3
∠UTV
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BigIdeasCh11Notes
11.3AreasofPolygonsRhombus KiteNamesomeproper@es: Namesomeproper@es:
AreaofRhombusorKite
A= Computeeacharea
RegularPolygon
CenterofaRegularPolygon:
Radius:
Apothem:
CentralAngle:
Whatisspecialabout∆ABFtotheright?
Solvefortheseanglesa)�
b)�
c)�
Areaofaregularpolygon=
m∠AFB
m∠AFG
m∠GAF
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BigIdeasCh11Notes
11.4Three-DimensionalFigures
Solids
Face:
Edge:
Vertex:
Polyhedron:
NotPolyhedron:
PolyhedraPrismDefini@on:
PyramidDefini@on:
Nameofsoliduses______________________________________________
Non-PolyhedraCylinderDefini@on:
ConeDefini@on:
SphereDefini@on:
CrossSecKonDefini@on:
Describethecrosssec@ons.
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BigIdeasCh11Notes
SolidofRevoluKonAthree-dimensionalfigurethatisformedby___________________________________________________________________.
Example:Iden@fythesolidcreatedbyrevolvingthetrianglearoundtheaxis(figureontheright).
11.5VolumesofPrismsandCylinders
Defini@onofVolume:
FormulaVolumeofaPrism: V=
Cavalieri’sPrinciple:
FormulaVolumeofaCylinder: V=
Calculatethevolumeofeachsolid.
DensityDefini@on:
FormulaDensity=
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BigIdeasCh11Notes
VolumeExample
Youarebuildingarectangularchest.Youwantthelengthtobe6feet,thewidthtobe4feet,andthevolumetobe72cubicfeet.Whatshouldtheheightbe?
SimilarSolidsTwosolidsofthesametype,likecylinders,with_____________________________ofcorrespondinglinearmeasures,suchas
__________________or________________,arecalled__________________________.
Thera@oofthecorrespondinglinearmeasuresoftwosimilarsolidsiscalledthe_______________________________________.
ExampleCylindersAandBaresimilar. a)Whatisthescalefactor?
b)WhatisthevolumeofcylinderB?
VolumeofCompositeSolidComputethevolumeoftheconcreteblock.Thetwoholesgoallthewaythrough.
11.6VolumesofPyramids
VolumeofaPyramid
Formula V=
Regularand__________________pyramidshavethesame___________________andthesame
______________________________areaateverylevel,then_____________________Principle
saystheyhavethesame______________________.
ExampleKhafre’sPyramidhadaheightofabout144metersandavolumeofabout2,218,800cubicmeters.Findthesidelengthofthesquarebase.
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BigIdeasCh11Notes
ExamplePyramidsAandBaresimilar.a)Whatisthescalefactor? b)WhatisthevolumeofpyramidB?
VolumeofCompositeSolidComputethevolumeofthecompositefigure.
11.7SurfaceAreasandVolumesofCones
Cones
Base: SlantHeight(l):
Vertex: LateralSurface:
Height:
Formulas LateralSurfaceAreaofaRightCone=L=
SurfaceAreaofaRightCone=S=
VolumeofaCone=V=
ExampleComputethesurfaceareaandvolumeofthecompositefiguretotheright.
SimilarSolidsExampleConesAandBaresimilar.
a)Whatisthescalefactor? b)WhatisthevolumeofconeB?
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BigIdeasCh11Notes
11.8SurfaceAreasandVolumesofSpheres
DefiniKonsCenter:
Radius:
Chord:
GreatCircle:
Hemisphere:
FormulasSurfaceAreaofaSphere=S=
VolumeofaSphere=V=
a)Computethesurfaceareaandvolumeofthesoccerball.
b)Computethesurfaceareaandvolumeofthecompositefigure.(Cylinderwithhemispherecutout.)
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