Chapter 11 Circumference, Area, and Volume 11.1 ... Ideas Ch...11.8 Surface Areas and Volumes of...
Transcript of Chapter 11 Circumference, Area, and Volume 11.1 ... Ideas Ch...11.8 Surface Areas and Volumes of...
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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