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Page 1: Click to LEARN this concept/topic on Doubtnut · CONCEPT FOR BOARDS || Chapter SURFACE AREAS AND VOLUMES 3. SURFACE AREAS AND VOLUMES OF COMBINATIONS OF SOLIDS 2. Combination of sphere

BOARDSCONCEPTSBOOSTER

SURFACEAREASANDVOLUMES

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1

CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

1.Reviewfrompreviousclass

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2

CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

2.Cuboid

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3

CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

3.Cube

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Page 2: Click to LEARN this concept/topic on Doubtnut · CONCEPT FOR BOARDS || Chapter SURFACE AREAS AND VOLUMES 3. SURFACE AREAS AND VOLUMES OF COMBINATIONS OF SOLIDS 2. Combination of sphere

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

4.RightCircularCylinder

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

5.RightCircularhollowcylinder

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

6.RightCircularCone

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

7.SphereandHemisphere

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

1.INTRODUCTION

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Page 3: Click to LEARN this concept/topic on Doubtnut · CONCEPT FOR BOARDS || Chapter SURFACE AREAS AND VOLUMES 3. SURFACE AREAS AND VOLUMES OF COMBINATIONS OF SOLIDS 2. Combination of sphere

8 8.SphericalShell

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

1.Conversionof cube into cuboidby Joining :Twocubeseachof 10 cmedgearejoinedendtoend.Findthesurfaceareaandvolumeofcuboid.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

2.Conversionof cubesbyMeltingandRecasting :Threecubesaremelted,whoseedges are to form a single cube. Find its edge; volume andsurfacearea.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

3.ConversionofSphereintocylinder:Thediameterofmetallicsphereis6cm.It ismeltedanddrawnintoawirehavingdiameterofthecrosssectionas0.2cm.Findthelengthofthewire.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

4.WaterFlowProblems :ACylindericalpipehas innerdiameterof7cmandwaterflowsthroughitat192.5litresperminute.Findtherateofflowinkilometersperhour.

3cm, 4cm and 5cm

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13

CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

5.ConversionofSolidbyMeltingandRecasting

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

6.ConversionofSolidbyshapechange

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

2.CONVERSIONOFSOLIDS

7.Raiseinwaterlevelproblems:Acylindricaltubofradius12cmcontainswatertoadepthof20cm.Asphericalformballofaradius9cmisdroppedintothetubandthusthelevelofwaterisraisedbyHcm.WhatisthevalueofH?

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

1.Combinationofcylinderandcone:ACirculartentiscylindricaluptoaheightof3mandconicalabove it. If thediameterof thebase is105mandtheslantheightof theconicalpartis53m;findthetotalcanvasusedinmakingthetent.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

2.Combinationofsphereandcone:Arightcircularcylinderhavingdiameter12cmandheight15cmisfullofice-cream.Theicecreamistobefilledinconesofheight12cmanddiameter6cmhavingahemisphericalshapeonthetop.Findthenumberofconeswhichcanbefilledwithice-cream.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

3.Combinationofcubeandcone:Findthevolumeofthelargestrightcircularconethatcanbecutoutofacubewhoseedgeis9cm.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

4.Combinationofcylinderandhemisphere :Asolid is in the formofacylinderwithhemisphericalends.Thethewholelengthofthesolidis108cmandthediameterofthehemisphericalendsis36cm;Findthecostofpolishingthesurfaceofthesolidsattherateof7paisepersq.cm.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

5.ARight trianglewhosesidesare15cmand20cm; ismade to revolveabout itshypotenuse.Findthevolumeandsurfaceareaofthedoubleconesoformed.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

3.SURFACEAREASANDVOLUMESOFCOMBINATIONSOFSOLIDS

6. combinations of more than two solids : A solid is in the form of a hemispheresurmountedbyarightcircularcone.Heightoftheconeis2cmandthediameterofthebaseis4cm.Ifarightcircularcylindercircumscribesthesolid.Findhowmuchmorespaceitwillcover.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

4.FRUSTUMOFRIGHTCIRCULARCONE

1.WhatisFrustum?HeightandslantheightofFrustum.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

4.FRUSTUMOFRIGHTCIRCULARCONE

2.VolumeofaFrustum

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

4.FRUSTUMOFRIGHTCIRCULARCONE

3.SurfaceAreaofaFrustum

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

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254.FRUSTUMOFRIGHTCIRCULARCONE

4.Importantpointsforfrustum

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

5.EXAMPLESOFFRUSTUM

1.AHollowconeiscutbyaplaneparalleltothebaseandupperportionisremoved.Ifthecurvedsurfaceof the remainder is8/9of thecurvedsurfaceof thewholecone;findtheratiooftheline-segmentintowhichthecone'saltitudeisdividedbytheplane.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

5.EXAMPLESOFFRUSTUM

2.Ashuttle cockused forplayingbadmintonhas theshapeofa frustumofa conemountedonahemisphere.Thediametersoftheendsofthefrustumare5cmand2cm;theheightoftheentireshuttlecockis7cm.Findtheexternalsurfacearea.

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CONCEPTFORBOARDS||ChapterSURFACEAREASANDVOLUMES

5.EXAMPLESOFFRUSTUM

3.Anoilfunnelmadeoftinsheetconsistsofa10cmlongcylindricalportionattachedtoafrustumofacone.Ifthetotalheightis22cm;diameterofthecylindricalportionis8cmandthediameterofthetopofthefunnelis18cm;findtheareaofthetinsheetrequiredtomakethefunnel.

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