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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