SlideShare a Scribd company logo
1 of 29
Assignment (FA-3)
Submitted to :- Sh. BharatBhushan Sir
Submitted by :- Nitin Chhaperwal
Class IX
Roll No. 915
Kendriya Vidyalaya SSTPS
Topic – Surface
Areas and Volumes
Contents :-
CUBE AND CUBOID
face
face
face
Total faces = 6 ( Here three faces are visible)
1
2 3
Dice (Pasa)
Faces of cube
Faces of Parallelopiped
Brick
Book
Face
Face
Face
Total faces = 6 ( Here only three faces are visible.)
Cores
Total cores = 12 ( Here only 9 cores are visible)
Cores
Note Same is in the case in parallelopiped.
Surface area = Area of all six faces
= 6a2
a
b
Surface area
Cube Parallelopiped (Cuboid)
Surface area = Area of all six faces
= 2(axb + bxc +cxa)
c
a
a
a
Click to see the faces of
parallelopiped.
(Here all the faces are square) (Here all the faces are rectangular)
Area of base (rectangle) = a x b
a
Height of cuboid = c
Volume of cube = Area of base x height
= (a x b) x c
b
c
b
Volume of Parallelopiped Click to animate
Volume of Cube
a
a
Area of base (square) = a2
Height of cube = a
Volume of cube = Area of base x height
= a2
x a = a3
Click to see
a
(unit)3
CYLINDER
Circumference of circle = 2 π r
Area covered by cylinder = Surface area of cylinder = (2 π r) x( h)
r
h
Outer Curved Surface area of cylinder
Activity -: Keep
bangles of same
radius one over
another. It will
form a cylinder.
It is the area covered by the outer surface of a cylinder.
Formation of Cylinder
by bangles
Circumference of
circle = 2 π r
r
Click to animate
Total Surface area of a solid cylinder
=(2 π r) x( h) + 2 π r2
Curved
surface
Area of curved surface + area of two circular surfaces=
circular
surfaces
= 2 π r( h+ r)
2πr
h
r
h
Surface area of cylinder = Area of rectangle= 2 πrh
Other method of Finding Surface area of cylinder with the help of paper
Volume of cylinder
Volume of cylinder = Area of base x vertical height
= π r2
x h
r
h
Base
r
h
l=Slantheight
CONE
3( V ) = π r2
h
r
h h
r
Volume of a Cone
Click to See
the experiment
Here the vertical height and
radius of cylinder & cone are
same.
3( volume of cone) = volume of cylinder
V = 1/3 π r2
h
If both cylinder and cone have same height
and radius then volume of a cylinder is three
times the volume of a cone ,
Volume = 3V Volume =V
Mr. Mohan has only a little jar of juice he wants to distribute it
to his three friends. This time he choose the cone shaped
glass so that quantity of juice seem to appreciable.
l
2πr
l
2πr
l
Area of a circle having sector (circumference) 2π l = π l 2
Area of circle having circumference 1 =
π l 2
/ 2 π l
So area of sector having sector 2 π r = (π l 2
/ 2 π l )x 2 π r = π rl
Surface area of cone
Think :- Which shape (cone or cylindrical) is better for
collecting resin from the tree?
Click the next
r
3r
V= 1/3π r2
(3r)
V= π r3
Long but Light in weight
Small needle will
require to stick it
in the tree, so little
V= π r2
(3r)
V= 3 π r3
Long but Heavy in weight
Long needle will
require to stick it in
the tree, so much
r
SPHERE
A sphere is the set of points in three
dimensions that are a fixed distance from
a given point, the center. A plane that
intersects a sphere through its center
divides the two halves or hemispheres.
The edge of a hemisphere is a great
circle.
Sphere
The volume of a hemisphere is
exactly halfway between the
volume of a cone and a cylinder
with the same radius r and
height equal to r.
V1
r
V=1/3 πr2
h
If h = r then
V=1/3 πr3
r
If we make a cone having radius and height equal to
the radius of sphere. Then a water filled cone can fill
the sphere in 4 times.
V1 = 4V = 4(1/3 πr3
)
= 4/3 πr3
4( 1/3πr2
h ) = 4( 1/3πr3
) = V
h=r
r
Volume of a Sphere
Here the vertical height and
radius of cone are same as
radius of sphere.
4( volume of cone) = volume of Sphere
V = 4/3 π r3
r
Click to See
the experiment
The surface area of a sphere is four
times the area of a great circle.
≈ 50.3 units2
THANK YOU

More Related Content

What's hot

Surface Area Of Solids
Surface Area Of SolidsSurface Area Of Solids
Surface Area Of Solids
joannahstevens
 
3 d figures, its surface areas and volumes
3 d figures, its surface areas and volumes3 d figures, its surface areas and volumes
3 d figures, its surface areas and volumes
jeevanlata
 
surface area and volume
surface area and volumesurface area and volume
surface area and volume
abhinavaaaa
 
Surface Area Of Solids Cps
Surface Area Of Solids CpsSurface Area Of Solids Cps
Surface Area Of Solids Cps
kliegey524
 
3D Figures- volume and surface area
3D Figures- volume and surface area3D Figures- volume and surface area
3D Figures- volume and surface area
Renegarmath
 
Geom12point2and3 97
Geom12point2and3 97Geom12point2and3 97
Geom12point2and3 97
herbison
 

What's hot (20)

SURFACE AREA AND VOLUME
SURFACE AREA AND VOLUMESURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME
 
C8: Surface Area and Volume
C8: Surface Area and VolumeC8: Surface Area and Volume
C8: Surface Area and Volume
 
surface area and volume ppt
surface area and volume ppt surface area and volume ppt
surface area and volume ppt
 
Surface Area Of Solids
Surface Area Of SolidsSurface Area Of Solids
Surface Area Of Solids
 
Surface area and volume for 9th class maths
Surface area and volume for 9th class mathsSurface area and volume for 9th class maths
Surface area and volume for 9th class maths
 
Volume and Surface Areas
Volume and Surface AreasVolume and Surface Areas
Volume and Surface Areas
 
Surface area and volume
Surface area and volumeSurface area and volume
Surface area and volume
 
surface area and volumes class 9th
surface area and volumes class 9thsurface area and volumes class 9th
surface area and volumes class 9th
 
Surface area and volume ssolids
Surface area and volume ssolidsSurface area and volume ssolids
Surface area and volume ssolids
 
Power point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARIPower point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARI
 
3 d figures, its surface areas and volumes
3 d figures, its surface areas and volumes3 d figures, its surface areas and volumes
3 d figures, its surface areas and volumes
 
Mensuration
MensurationMensuration
Mensuration
 
surface area and volume
surface area and volumesurface area and volume
surface area and volume
 
Surface Area Of Solids Cps
Surface Area Of Solids CpsSurface Area Of Solids Cps
Surface Area Of Solids Cps
 
Surface areas and volumes
Surface areas and volumesSurface areas and volumes
Surface areas and volumes
 
3D Figures- volume and surface area
3D Figures- volume and surface area3D Figures- volume and surface area
3D Figures- volume and surface area
 
Basic Mensuration
Basic MensurationBasic Mensuration
Basic Mensuration
 
Mensuration
MensurationMensuration
Mensuration
 
Geom12point2and3 97
Geom12point2and3 97Geom12point2and3 97
Geom12point2and3 97
 
Surface area and volume of a cylinder
Surface area and volume of a cylinderSurface area and volume of a cylinder
Surface area and volume of a cylinder
 

Viewers also liked

Innovative Team Selling, Eric Baron's Latest Book
Innovative Team Selling, Eric Baron's Latest BookInnovative Team Selling, Eric Baron's Latest Book
Innovative Team Selling, Eric Baron's Latest Book
innovativeteamselling
 
The road not taken-Robert Frost
The road not taken-Robert FrostThe road not taken-Robert Frost
The road not taken-Robert Frost
Nitin Chhaperwal
 

Viewers also liked (13)

Chemical reactions
Chemical reactionsChemical reactions
Chemical reactions
 
Power Sharing
Power SharingPower Sharing
Power Sharing
 
Congruent triangles
Congruent trianglesCongruent triangles
Congruent triangles
 
Finger printing
Finger printingFinger printing
Finger printing
 
Rain water harvesting
Rain water harvestingRain water harvesting
Rain water harvesting
 
Matrices
MatricesMatrices
Matrices
 
Straightpoint ATEX & IECEx load monitoring products for hazardous areas
Straightpoint ATEX & IECEx load monitoring products for hazardous areasStraightpoint ATEX & IECEx load monitoring products for hazardous areas
Straightpoint ATEX & IECEx load monitoring products for hazardous areas
 
vedic mathematics
vedic mathematics vedic mathematics
vedic mathematics
 
Innovative Team Selling, Eric Baron's Latest Book
Innovative Team Selling, Eric Baron's Latest BookInnovative Team Selling, Eric Baron's Latest Book
Innovative Team Selling, Eric Baron's Latest Book
 
The road not taken-Robert Frost
The road not taken-Robert FrostThe road not taken-Robert Frost
The road not taken-Robert Frost
 
Subordinating conjunction
Subordinating conjunctionSubordinating conjunction
Subordinating conjunction
 
Famous Mathematicians
Famous MathematiciansFamous Mathematicians
Famous Mathematicians
 
Newton's laws of motion
Newton's laws of motionNewton's laws of motion
Newton's laws of motion
 

Similar to Surface areas and volumes

Surface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.pptSurface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.ppt
LuisSalenga1
 
Volume of sphere[1]
Volume of sphere[1]Volume of sphere[1]
Volume of sphere[1]
Poonam Singh
 
Three dimensional geometry
Three dimensional geometryThree dimensional geometry
Three dimensional geometry
Anthony_Maiorano
 
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
VigneshKaushik1
 

Similar to Surface areas and volumes (20)

Area and Volume
Area and VolumeArea and Volume
Area and Volume
 
Mensuration
MensurationMensuration
Mensuration
 
Surface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.pptSurface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.ppt
 
Surface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.pptSurface Area_Volume of Solid Figures.ppt
Surface Area_Volume of Solid Figures.ppt
 
Surface areas and volumes ppt
Surface areas and volumes pptSurface areas and volumes ppt
Surface areas and volumes ppt
 
Rita Math ppt.pptx
Rita Math ppt.pptxRita Math ppt.pptx
Rita Math ppt.pptx
 
Measurement of Three Dimensional Figures _Module and test questions.
Measurement of Three Dimensional Figures _Module and test questions.Measurement of Three Dimensional Figures _Module and test questions.
Measurement of Three Dimensional Figures _Module and test questions.
 
Assessment forfolio questions
Assessment forfolio questionsAssessment forfolio questions
Assessment forfolio questions
 
Gre solid 02 math geo
Gre solid 02 math geoGre solid 02 math geo
Gre solid 02 math geo
 
Maths project
Maths projectMaths project
Maths project
 
Maths p.p.t
Maths  p.p.tMaths  p.p.t
Maths p.p.t
 
Cube, cuboid and cylinder
Cube, cuboid and cylinder Cube, cuboid and cylinder
Cube, cuboid and cylinder
 
Mensuration ppt in maths
Mensuration ppt in mathsMensuration ppt in maths
Mensuration ppt in maths
 
Volume of sphere[1]
Volume of sphere[1]Volume of sphere[1]
Volume of sphere[1]
 
Three dimensional geometry
Three dimensional geometryThree dimensional geometry
Three dimensional geometry
 
Volume and surface area
Volume and surface areaVolume and surface area
Volume and surface area
 
5.13.4 Surface Area
5.13.4 Surface Area5.13.4 Surface Area
5.13.4 Surface Area
 
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
𝗠𝗔𝗧𝗛𝗦 𝗣𝗥𝗢𝗝𝗘𝗖𝗧.pdf
 
Obj. 45 Surface Area
Obj. 45 Surface AreaObj. 45 Surface Area
Obj. 45 Surface Area
 
MENSURATION
MENSURATIONMENSURATION
MENSURATION
 

More from Nitin Chhaperwal (9)

Rain water harvesting - Need of the era
Rain water harvesting - Need of the eraRain water harvesting - Need of the era
Rain water harvesting - Need of the era
 
Jokes...;)
Jokes...;)Jokes...;)
Jokes...;)
 
Fundamental rights
Fundamental rightsFundamental rights
Fundamental rights
 
Villa for sale Class IX
Villa for sale Class IX Villa for sale Class IX
Villa for sale Class IX
 
Role of education
Role of educationRole of education
Role of education
 
कबीर दास
कबीर दासकबीर दास
कबीर दास
 
Fundamental rights and the duties
Fundamental rights and the dutiesFundamental rights and the duties
Fundamental rights and the duties
 
Srinivasa Ramanujan and his magic square
Srinivasa Ramanujan and his magic squareSrinivasa Ramanujan and his magic square
Srinivasa Ramanujan and his magic square
 
Great ancient indians
Great ancient indiansGreat ancient indians
Great ancient indians
 

Recently uploaded

The basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptxThe basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptx
heathfieldcps1
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
中 央社
 

Recently uploaded (20)

DEMONSTRATION LESSON IN ENGLISH 4 MATATAG CURRICULUM
DEMONSTRATION LESSON IN ENGLISH 4 MATATAG CURRICULUMDEMONSTRATION LESSON IN ENGLISH 4 MATATAG CURRICULUM
DEMONSTRATION LESSON IN ENGLISH 4 MATATAG CURRICULUM
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
 
An overview of the various scriptures in Hinduism
An overview of the various scriptures in HinduismAn overview of the various scriptures in Hinduism
An overview of the various scriptures in Hinduism
 
e-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopale-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopal
 
How to Analyse Profit of a Sales Order in Odoo 17
How to Analyse Profit of a Sales Order in Odoo 17How to Analyse Profit of a Sales Order in Odoo 17
How to Analyse Profit of a Sales Order in Odoo 17
 
The basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptxThe basics of sentences session 4pptx.pptx
The basics of sentences session 4pptx.pptx
 
Improved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio AppImproved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio App
 
Graduate Outcomes Presentation Slides - English (v3).pptx
Graduate Outcomes Presentation Slides - English (v3).pptxGraduate Outcomes Presentation Slides - English (v3).pptx
Graduate Outcomes Presentation Slides - English (v3).pptx
 
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
 
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
 
How To Create Editable Tree View in Odoo 17
How To Create Editable Tree View in Odoo 17How To Create Editable Tree View in Odoo 17
How To Create Editable Tree View in Odoo 17
 
PSYPACT- Practicing Over State Lines May 2024.pptx
PSYPACT- Practicing Over State Lines May 2024.pptxPSYPACT- Practicing Over State Lines May 2024.pptx
PSYPACT- Practicing Over State Lines May 2024.pptx
 
Basic Civil Engineering notes on Transportation Engineering, Modes of Transpo...
Basic Civil Engineering notes on Transportation Engineering, Modes of Transpo...Basic Civil Engineering notes on Transportation Engineering, Modes of Transpo...
Basic Civil Engineering notes on Transportation Engineering, Modes of Transpo...
 
Including Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdfIncluding Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdf
 
demyelinated disorder: multiple sclerosis.pptx
demyelinated disorder: multiple sclerosis.pptxdemyelinated disorder: multiple sclerosis.pptx
demyelinated disorder: multiple sclerosis.pptx
 
Andreas Schleicher presents at the launch of What does child empowerment mean...
Andreas Schleicher presents at the launch of What does child empowerment mean...Andreas Schleicher presents at the launch of What does child empowerment mean...
Andreas Schleicher presents at the launch of What does child empowerment mean...
 
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptxAnalyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
 
Spring gala 2024 photo slideshow - Celebrating School-Community Partnerships
Spring gala 2024 photo slideshow - Celebrating School-Community PartnershipsSpring gala 2024 photo slideshow - Celebrating School-Community Partnerships
Spring gala 2024 photo slideshow - Celebrating School-Community Partnerships
 
Mattingly "AI and Prompt Design: LLMs with Text Classification and Open Source"
Mattingly "AI and Prompt Design: LLMs with Text Classification and Open Source"Mattingly "AI and Prompt Design: LLMs with Text Classification and Open Source"
Mattingly "AI and Prompt Design: LLMs with Text Classification and Open Source"
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
 

Surface areas and volumes

  • 1. Assignment (FA-3) Submitted to :- Sh. BharatBhushan Sir Submitted by :- Nitin Chhaperwal Class IX Roll No. 915 Kendriya Vidyalaya SSTPS Topic – Surface Areas and Volumes
  • 4. face face face Total faces = 6 ( Here three faces are visible) 1 2 3 Dice (Pasa) Faces of cube
  • 5. Faces of Parallelopiped Brick Book Face Face Face Total faces = 6 ( Here only three faces are visible.)
  • 6. Cores Total cores = 12 ( Here only 9 cores are visible) Cores Note Same is in the case in parallelopiped.
  • 7. Surface area = Area of all six faces = 6a2 a b Surface area Cube Parallelopiped (Cuboid) Surface area = Area of all six faces = 2(axb + bxc +cxa) c a a a Click to see the faces of parallelopiped. (Here all the faces are square) (Here all the faces are rectangular)
  • 8. Area of base (rectangle) = a x b a Height of cuboid = c Volume of cube = Area of base x height = (a x b) x c b c b Volume of Parallelopiped Click to animate
  • 9. Volume of Cube a a Area of base (square) = a2 Height of cube = a Volume of cube = Area of base x height = a2 x a = a3 Click to see a (unit)3
  • 11. Circumference of circle = 2 π r Area covered by cylinder = Surface area of cylinder = (2 π r) x( h) r h Outer Curved Surface area of cylinder Activity -: Keep bangles of same radius one over another. It will form a cylinder. It is the area covered by the outer surface of a cylinder. Formation of Cylinder by bangles Circumference of circle = 2 π r r Click to animate
  • 12. Total Surface area of a solid cylinder =(2 π r) x( h) + 2 π r2 Curved surface Area of curved surface + area of two circular surfaces= circular surfaces = 2 π r( h+ r)
  • 13. 2πr h r h Surface area of cylinder = Area of rectangle= 2 πrh Other method of Finding Surface area of cylinder with the help of paper
  • 14. Volume of cylinder Volume of cylinder = Area of base x vertical height = π r2 x h r h
  • 16. 3( V ) = π r2 h r h h r Volume of a Cone Click to See the experiment Here the vertical height and radius of cylinder & cone are same. 3( volume of cone) = volume of cylinder V = 1/3 π r2 h
  • 17. If both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone , Volume = 3V Volume =V
  • 18. Mr. Mohan has only a little jar of juice he wants to distribute it to his three friends. This time he choose the cone shaped glass so that quantity of juice seem to appreciable.
  • 19. l 2πr l 2πr l Area of a circle having sector (circumference) 2π l = π l 2 Area of circle having circumference 1 = π l 2 / 2 π l So area of sector having sector 2 π r = (π l 2 / 2 π l )x 2 π r = π rl Surface area of cone
  • 20. Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree? Click the next
  • 21. r 3r V= 1/3π r2 (3r) V= π r3 Long but Light in weight Small needle will require to stick it in the tree, so little V= π r2 (3r) V= 3 π r3 Long but Heavy in weight Long needle will require to stick it in the tree, so much r
  • 23. A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle. Sphere
  • 24. The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.
  • 25.
  • 26. V1 r V=1/3 πr2 h If h = r then V=1/3 πr3 r If we make a cone having radius and height equal to the radius of sphere. Then a water filled cone can fill the sphere in 4 times. V1 = 4V = 4(1/3 πr3 ) = 4/3 πr3
  • 27. 4( 1/3πr2 h ) = 4( 1/3πr3 ) = V h=r r Volume of a Sphere Here the vertical height and radius of cone are same as radius of sphere. 4( volume of cone) = volume of Sphere V = 4/3 π r3 r Click to See the experiment
  • 28. The surface area of a sphere is four times the area of a great circle. ≈ 50.3 units2