SlideShare a Scribd company logo
1 of 85
Download to read offline
K.V
    Faridkot
Harkamalpreet
Singh Brar
   9 -B
     th
Topic
Objectives
 At the end of the lesson the students
  should be able;
      To find the surface area of a
  cylinder ..
What is a cylinder?
 The term Cylinder refers to a right
  circular cylinder. Like a right prism, its
  altitude is perpendicular to the bases
  and has an endpoint in each base.
PRESENTATION

          base



          altitude

        radius

        base
What will happen if we
 removed the end of the
cylinder and unrolled the
          body?

  Lets find out
 !!!!
This will happen if we unrolled
  and removed the end of a
          cylinder….



                           h
           Circumference
           of the base
2Πr   2
Notice that we had formed 2
 circles and a 1 rectangle….


 The 2 circles serves as our bases of
  our cylinder and the rectangular
  region represent the body
How can we solved the surface
    area of a Cylinder?

 To solve the surface area of a
  cylinder, add the areas of the
  circular bases and the area of
  the rectangular region which is
  the body of the cylinder.
This is the formula in order to
 solved the surface are of a
           cylinder.

 SA= area of 2 circular bases
  + are of a rectangle


              oR
We derived at this formula..!!

SA=2Πr2 +2Πr
           Or

          SA=2Πr (r + h)
Find the surface area of a
 cylindrical water tank given the
 height of 20m and the radius of
       5m? (Use π as 3.14)
Given:
         SA=2πr2 +2πrh
h=20m
r=5m        =2(3.14)(5m)2 + 2[(3.14)
         (5m)(20m)
           =157m2 + 628m
         SA =785m2
2-Surface Area of a Prism
    Cubes and Cuboids
Surface area of a cuboid

 To find the surface area of a shape, we calculate the
 total area of all of the faces.



                             A cuboid has 6 faces.


                             The top and the bottom of the
                             cuboid have the same area.
Surface area of a cuboid

 To find the surface area of a shape, we calculate the
 total area of all of the faces.



                             A cuboid has 6 faces.


                             The front and the back of the
                             cuboid have the same area.
Surface area of a cuboid

 To find the surface area of a shape, we calculate the
 total area of all of the faces.



                             A cuboid has 6 faces.


                             The left hand side and the right
                             hand side of the cuboid have
                             the same area.
Surface area of a cuboid

 To find the surface area of a shape, we calculate the
 total area of all of the faces.
                                    Can you work out the
                        5 cm
       8 cm                      surface area of this cubiod?

                              The area of the top = 8 × 5
                                                  = 40 cm2
7 cm                          The area of the front = 7 × 5
                                                    = 35 cm2
                              The area of the side = 7 × 8
                                                   = 56 cm2
Surface area of a cuboid

 To find the surface area of a shape, we calculate the
 total area of all of the faces.

                    5 cm     So the total surface area =
       8 cm

                              2 × 40 cm2    Top and bottom

7 cm                         + 2 × 35 cm2 Front and back


                             + 2 × 56 cm2 Left and right side

                             = 80 + 70 + 112 = 262 cm2
Formula for the surface area of a cuboid

 We can find the formula for the surface area of a cuboid
 as follows.
                              Surface area of a cuboid =
                    w
        l
                             2 × lw         Top and bottom


 h                           + 2 × hw       Front and back


                             + 2 × lh       Left and right side

                             = 2lw + 2hw + 2lh
Surface area of a cube


   How can we find the surface area of a cube of length x?

                          All six faces of a cube have the
                          same area.

                          The area of each face is x × x = x2

                          Therefore,

      x
                             Surface area of a cube = 6x2
Checkered cuboid problem

This cuboid is made from alternate purple and green
centimetre cubes.
                             What is its surface area?

                          Surface area
                          =2×3×4+2×3×5+2×4×5
                          = 24 + 30 + 40
                          = 94 cm2

                                How much of the
                              surface area is green?
                                     48 cm2
Surface area of a prism

          What is the surface area of this L-shaped prism?
                3 cm
                                   To find the surface area of
   3 cm
                                   this shape we need to add
                                   together the area of the two
                         4 cm      L-shapes and the area of the
                                   6 rectangles that make up
6 cm                               the surface of the shape.

                                   Total surface area
                                   = 2 × 22 + 18 + 9 + 12 + 6
                                     + 6 + 15
             5 cm                  = 110 cm2
Using nets to find surface area

 It can be helpful to use the net of a 3-D shape to calculate its
 surface area.
 Here is the net of a 3 cm by 5 cm by 6 cm cubiod.
                6 cm
                                                  Write down the
                                                  area of each
      3 cm     18 cm2     3 cm
                                     6 cm         face.
                                                  Then add the
5 cm 15 cm2    30 cm2     15 cm2    30 cm2
                                                  areas together
                                                  to find the
                                                  surface area.
      3 cm     18 cm2     3 cm
                                     Surface Area = 126 cm2
Using nets to find surface area

 Here is the net of a regular tetrahedron.

                    What is its surface area?

                                Area of each face = ½bh
                                                  = ½ × 6 × 5.2

                                                  = 15.6 cm2

 5.2 cm                              Surface area = 4 × 15.6
                                                  = 62.4 cm2
             6 cm
3-Warm up: Finding the Area of a
Lateral Face
 Architecture. The lateral faces of the
  Pyramid Arena in Memphis, Tennessee,
  are covered with steal panels. Use the
  diagram of the arena to find the area of
  each lateral face of this regular pyramid.
Pyramid Arena




mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
Surface Area of a Cone


                                           Unit 6, Day 4
                                            Ms. Reed
With slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of
   %20Pyramids%20and%20Cones%20C...
 A cone has a circular base and a vertex that is not in the same plane as
  a base.
 In a right cone, the height meets the base at its center.

                                                       The vertex is directly
                         Height                        above the center of
                                                       the circle.
                          Lateral Surface
                                                          Slant Height


                     r
        Base
                                                      r

 The height of a cone is the perpendicular distance between the vertex
  and the base.
 The slant height of a cone is the distance between the vertex and a
  point on the base edge.
Surface Area of a Cone
 Surface Area = area of base + area of sector


  = area of base + π(radius of base)(slant height)



         S = B + π r l = π r + π rl      2




                             l

  B =πr      2           r
Lateral Area of a Cone
 Since Lateral Area = Surface Area – area of the
  base



           = π r + π rl
            L.A. = 2
Example 1:
 Find the surface area of the cone to the nearest
   whole number.
a.     4 in.                 r = 4 slant height = 6
                            S = π r + π rl
                                    2

                               = π (4) + π (4)(6)
                                        2
     6 in.

                               = 16π + 24π
                               = 40π
                               = 40(3.14)
                               ≈ 126in.     2
Example 2:
 Find the surface area of the cone to the nearest whole
  number.
b.                               l
               5 ft.


                        12 ft.



First, find the slant height.        Next, r = 12,   l = 13.
l =r +h
 2      2      2                     S = π r + π rl
                                                2

  = (12) + (5)
        2      2                         = π (12) + π (12)(13)
                                             2


     = 144 + 25 = 169                    = 144π + 156π
                                         = 300π
l = 169 = 13                             ≈ 942 ft.    2
On your own #1
     Calculate the surface
       area of:

         S = π r 2 + π rl


•S = π(7)2 + π(7)(11.40)
•S = 49π + 79.80π
•S = 128.8π
On your own #2
Calculate the lateral area of:



   S   = π r = π rl
          L.A. +
             2




  •L.A. = π(5)(13)
  •L.A. = 65π
Homework
Work Packet:
Surface Area of Cones
4-Surface Area of a
      Sphere
Sphere
Hemisphere
Great Circle
(Surface Area of a Sphere) = 4πr2
5-Basic Geometric
   Properties


      Volume of a
        cuboid
In this lesson you will learn
to calculate the volume of a
           cuboid
Cuboids
Look at this cuboid


Now imagine it is full
of cubic centimetres
                                                                  6 cm



     1 cm3

                                                           4 cm

                                   10 cm


Can you see that there are 10 × 4 = 40 cubic centimetres on the
bottom layer?


There are 6 layers of 40 cubes making 40 × 6 = 240 cm3
Let us go back and look at what we did here




                                                      6 cm
                                                      height




                                                 4 cm
                                                breadth
                             10 cm
                            length


When we worked out the volume we multiplied the length by the
breadth and then by the height
Volume of a cuboid = length × breadth × height
                       or

                    V=lbh
Lets us look again
at the same
cuboid and this                                                     6 cm
time try the
formula

                                                             4 cm

                                   10 cm



                        V=lbh

                           = 10 × 4 × 6 cm3

                           = 240 cm3
You will see that this is the same answer as we got before
6-Volume of a Cylinder
What is Volume?

 The volume of a three-dimensional figure
  is the amount of space within it.

 Measured in Units Cubed (e.g. cm3)
Volume of a Prism
 Volume of a Prism is calculated by

Volume = Area of cross section x perpendicular height

  V = Ah

  V = (4 x 4) x 4 = 64 m3
What is this?
 It has 2 equal shapes at the base, but it is
  not a prism as it has rounded sides


It is a Cylinder
Volume of a Cylinder
 How might we find the Volume of a
  Cylinder?
Example
 V = Ah
Pieces Missing
 Find the volume of concrete used to make this
  pipe
 Volume of Concrete = Volume of Big
  Cylinder – Volume of Small Cylinder (hole)
 What shape is present here?
 What 3D shapes can you see?
HOME WORK




Find the Volume of the Solid. To 1 decimal place
Homework/Challenge
 Challenge Question
Volume of a Cylinder
 How might we find the Volume of a
  Cylinder?
 V = Ah
  –=
Conversion of units
 1cm – 10mm
 1m – 100cm
 1km – 1000m
Conversions of Units
1 cm2 = 10 mm x 10 mm      =100 mm2


1 m2   = 100 cm x 100 cm   = 10 000 cm2


1 m2   = 1000 mm x 1000 mm = 1 000 000 mm2


1 ha   = 100 m x 100 m     = 10 000 m2


1 km2 = 100 ha
What about when cubic units?
 1 cm3
 = 1cm x 1cm x 1cm
 = 10 mm × 10 mm × 10 mm
 = 1000 mm3

 1 m3
 = 1m x 1m x 1m
 = 100 cm × 100 cm × 100 cm
 = 1 000 000 cm3
Capacity
 Volume - The volume of a three-dimensional
  figure is the amount of space within it.
 Measured in Units Cubed (e.g. cm3)
 Volume and capacity are related.
 Capacity is the amount of material (usually
  liquid) that a container can hold.
 Capacity is measured in millilitres, litres and
  kilolitres.
Examples of Capacity
How does Volume relate to
              Capacity?
 1000 mL = 1 L

 1000 L = 1 kL

 1 cm3 = 1 mL

 1,000cm3 = 1000ml = 1L

 1 m3 = 1000 L = 1 kL
Examples
 Convert 1800 mL to L
 1800ml = 1800/1000
          = 1.8L

 2.3 m3 to L            1m3 = 1000L
  (1kL)
 2.3m3 = 2.3kL
         = 2300L
Length = 5.53cm


                Capacity
 Find the Capacity of this cube
 Length = 5.53cm

 V = Ah
 = (5.53 x 5.53) x 5.53
 = 169.11cm3                      (1cm3 =
  1ml)

 Capacity = 169.11ml
Example
 Find the capacity of this rectangular prism.
 Solution
 Volume = Ah
 = (26 x 12) x5
 = 312 × 5
 = 1560 cm3                       (1cm3 = 1mL)

 Capacity = 1560 mL or 1.56 L        (1000mL
  = 1L)
Ex 11.08 – Q 7.
 What size rainwater tank would be needed to
  hold the run-off when 40 mm of rain falls on a
  roof 12 m long and 3.6 m wide? (Answer in
  litres.)
7-Volume of Cones
Volume of Cylinders
 Volume = Base x height
 V = Bh
                               B
 Base area = π r2                 r

                           h
Compare Cone and Cylinder
   Use plastic space figures.
   Fill cone with water.
   Pour water into cylinder.
   Repeat until cylinder is full.
                                 r       r




                                     h
Volume of Cone?

                        =


 3 cones fill the cylinder, so…
 Volume = ⅓ Base x height
Volume of Cone
   3 cones fill the cylinder
   Volume = ⅓ Base x height
   V = ⅓ Bh                    h = 7 cm
   Base area = π r2




 V = ⅓ (π . 2.5 2) . 7                    r =2.5 cm

 V = ⅓ 3.14 . 6.25 . 7
8-Developing the Formula for the
      Volume of a Sphere
Volume of a Sphere


 Using relational solids and pouring material we noted
 that the volume of a cone is the same as the volume of a
 hemisphere (with corresponding dimensions)
Using “math language” Volume (cone) = ½ Volume (sphere)
Therefore            2(Volume (cone)) = Volume (sphere)


       OR                                 =
                          +
Volume of a Sphere


We already know the formula for the volume of a cone.


                                 Volumecylinder
                  Volumecone =
                                       3


      OR                 =              ÷3
Volume of a Sphere
AND we know the formula for the volume of a cylinder


        Volumecylinder = ( Area of Base ) X (Height )




                                       Height
                          BASE
Volume of a Sphere

SUMMARIZING:
Volume (cylinder) = (Area Base) (height)
Volume (cone) = Volume (cylinder) /3

              =                ÷3

Volume (cone) = (Area Base) (height)/3

AND 2(Volume (cone)) = Volume (sphere)

     2X                 =
Volume of a Sphere
       2(Volume (cone)) = Volume (sphere)
      2X                 =
2(Area of Base) (height) /3= Volume (sphere)

        2( πr2)(h)/3= Volume (sphere)
                                                r
                    BUT h = 2r              h
                                                r
        2(πr )(2r)/3 = Volume(sphere)
             2




           4(πr3)/3 = Volume(sphere)
3
4π r 
            Volume of a Sphere       4 π r 3
  3                                     3




                                 3
                            4π r 
           Volumesphere   =
                              3


4 π r 3                             4 π r 3
   3                                    3
Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt

More Related Content

What's hot

4 Geometry Area and Perimeter
4 Geometry Area and Perimeter4 Geometry Area and Perimeter
4 Geometry Area and PerimeterLara Williams
 
Evaluating Algebraic Expressions
Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions
Evaluating Algebraic Expressionsbizarregirl
 
Quadrilateral presentation
Quadrilateral presentationQuadrilateral presentation
Quadrilateral presentationlambor chinee
 
Area and circumference of circles
Area and circumference of circlesArea and circumference of circles
Area and circumference of circlesElisaS91
 
Algebraic fractions
Algebraic fractionsAlgebraic fractions
Algebraic fractionsDeb
 
Square root
Square rootSquare root
Square rootrryan80
 
Perimeter & area presentation
Perimeter & area presentationPerimeter & area presentation
Perimeter & area presentationrodriguezbrenda
 
Area of triangle
Area of triangleArea of triangle
Area of trianglemonaliitkar
 
Presentation on inverse proportion
Presentation on inverse proportionPresentation on inverse proportion
Presentation on inverse proportionwajihatrq
 
Rates and Unit Rate
Rates and Unit RateRates and Unit Rate
Rates and Unit Rate23vanpelt
 
12.1 Solid Geometry
12.1 Solid Geometry12.1 Solid Geometry
12.1 Solid Geometrysmiller5
 
3D Figures- volume and surface area
3D Figures- volume and surface area3D Figures- volume and surface area
3D Figures- volume and surface areaRenegarmath
 
Square, rectangle, and its properties
Square, rectangle, and its properties Square, rectangle, and its properties
Square, rectangle, and its properties Azharlina Rizqi Ardina
 

What's hot (20)

4 Geometry Area and Perimeter
4 Geometry Area and Perimeter4 Geometry Area and Perimeter
4 Geometry Area and Perimeter
 
Evaluating Algebraic Expressions
Evaluating Algebraic ExpressionsEvaluating Algebraic Expressions
Evaluating Algebraic Expressions
 
Types of angles
Types of anglesTypes of angles
Types of angles
 
Quadrilateral presentation
Quadrilateral presentationQuadrilateral presentation
Quadrilateral presentation
 
Surface area and volume ssolids
Surface area and volume ssolidsSurface area and volume ssolids
Surface area and volume ssolids
 
Area and circumference of circles
Area and circumference of circlesArea and circumference of circles
Area and circumference of circles
 
Rectangles
RectanglesRectangles
Rectangles
 
Algebraic fractions
Algebraic fractionsAlgebraic fractions
Algebraic fractions
 
Algebraic fractions
Algebraic fractionsAlgebraic fractions
Algebraic fractions
 
Square root
Square rootSquare root
Square root
 
Area
AreaArea
Area
 
Perimeter & area presentation
Perimeter & area presentationPerimeter & area presentation
Perimeter & area presentation
 
Area of triangle
Area of triangleArea of triangle
Area of triangle
 
Presentation on inverse proportion
Presentation on inverse proportionPresentation on inverse proportion
Presentation on inverse proportion
 
Rates and Unit Rate
Rates and Unit RateRates and Unit Rate
Rates and Unit Rate
 
Angles
AnglesAngles
Angles
 
12.1 Solid Geometry
12.1 Solid Geometry12.1 Solid Geometry
12.1 Solid Geometry
 
3D Figures- volume and surface area
3D Figures- volume and surface area3D Figures- volume and surface area
3D Figures- volume and surface area
 
Volume of a cone
Volume of a coneVolume of a cone
Volume of a cone
 
Square, rectangle, and its properties
Square, rectangle, and its properties Square, rectangle, and its properties
Square, rectangle, and its properties
 

Similar to Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt

Surface area and volume of cuboids
Surface area and volume of cuboidsSurface area and volume of cuboids
Surface area and volume of cuboidsSantosh Kumar
 
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.pptLuisSalenga1
 
Ch 10 study guide
Ch 10 study guideCh 10 study guide
Ch 10 study guidemlabuski
 
Ch 10 study guide
Ch 10 study guideCh 10 study guide
Ch 10 study guidemlabuski
 
Module 7 geometry of shape and size
Module 7   geometry of shape and sizeModule 7   geometry of shape and size
Module 7 geometry of shape and sizedionesioable
 
Perimeter, area and volume
Perimeter, area and volumePerimeter, area and volume
Perimeter, area and volumeAnthony Abidakun
 
Class9 surface areas & volumes
Class9  surface areas & volumesClass9  surface areas & volumes
Class9 surface areas & volumesanantababu
 
Gre solid 02 math geo
Gre solid 02 math geoGre solid 02 math geo
Gre solid 02 math geoAntu Biswsa
 
Cube, cuboid and cylinder
Cube, cuboid and cylinder Cube, cuboid and cylinder
Cube, cuboid and cylinder sriranjini ks
 
Volume and Surface Areas
Volume and Surface AreasVolume and Surface Areas
Volume and Surface AreasVioletBlack11
 
surface area and volume
surface area and volumesurface area and volume
surface area and volumeabhinavaaaa
 
Tec 551 interactive activity part 2
Tec  551 interactive activity part 2Tec  551 interactive activity part 2
Tec 551 interactive activity part 2jforeman03
 
Chapter 10 practice test
Chapter 10 practice testChapter 10 practice test
Chapter 10 practice testmlabuski
 
Chapter 10 practice test
Chapter 10 practice testChapter 10 practice test
Chapter 10 practice testmlabuski
 
Power point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARIPower point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARIPiyush Bhandaari
 

Similar to Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt (20)

Surface area and volume of cuboids
Surface area and volume of cuboidsSurface area and volume of cuboids
Surface area and volume of cuboids
 
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
 
Ch 10 study guide
Ch 10 study guideCh 10 study guide
Ch 10 study guide
 
Ch 10 study guide
Ch 10 study guideCh 10 study guide
Ch 10 study guide
 
Module 7 geometry of shape and size
Module 7   geometry of shape and sizeModule 7   geometry of shape and size
Module 7 geometry of shape and size
 
9463138669|RMS Exam Coaching Center in Jalandhar|ANAND CLASSES
9463138669|RMS Exam Coaching Center in Jalandhar|ANAND CLASSES 9463138669|RMS Exam Coaching Center in Jalandhar|ANAND CLASSES
9463138669|RMS Exam Coaching Center in Jalandhar|ANAND CLASSES
 
Perimeter, area and volume
Perimeter, area and volumePerimeter, area and volume
Perimeter, area and volume
 
Class9 surface areas & volumes
Class9  surface areas & volumesClass9  surface areas & volumes
Class9 surface areas & volumes
 
Gre solid 02 math geo
Gre solid 02 math geoGre solid 02 math geo
Gre solid 02 math geo
 
Cube, cuboid and cylinder
Cube, cuboid and cylinder Cube, cuboid and cylinder
Cube, cuboid and cylinder
 
Soumya1
Soumya1Soumya1
Soumya1
 
Maths p.p.t
Maths  p.p.tMaths  p.p.t
Maths p.p.t
 
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
 
Tec 551 interactive activity part 2
Tec  551 interactive activity part 2Tec  551 interactive activity part 2
Tec 551 interactive activity part 2
 
Area
AreaArea
Area
 
Unit 2 3D Geometry
Unit 2 3D GeometryUnit 2 3D Geometry
Unit 2 3D Geometry
 
Chapter 10 practice test
Chapter 10 practice testChapter 10 practice test
Chapter 10 practice test
 
Chapter 10 practice test
Chapter 10 practice testChapter 10 practice test
Chapter 10 practice test
 
Power point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARIPower point presentation PIYUSH BHANDARI
Power point presentation PIYUSH BHANDARI
 

Recently uploaded

Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Celine George
 
How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17Celine George
 
Employablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptxEmployablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptxryandux83rd
 
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptx
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptxBIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptx
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptxSayali Powar
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Osopher
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWQuiz Club NITW
 
How to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseHow to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseCeline George
 
MS4 level being good citizen -imperative- (1) (1).pdf
MS4 level   being good citizen -imperative- (1) (1).pdfMS4 level   being good citizen -imperative- (1) (1).pdf
MS4 level being good citizen -imperative- (1) (1).pdfMr Bounab Samir
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...DhatriParmar
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...Nguyen Thanh Tu Collection
 
Comparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxComparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxAvaniJani1
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management SystemChristalin Nelson
 
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...Nguyen Thanh Tu Collection
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6Vanessa Camilleri
 

Recently uploaded (20)

Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17
 
How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17
 
Employablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptxEmployablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptx
 
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptx
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptxBIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptx
BIOCHEMISTRY-CARBOHYDRATE METABOLISM CHAPTER 2.pptx
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITW
 
Mattingly "AI & Prompt Design" - Introduction to Machine Learning"
Mattingly "AI & Prompt Design" - Introduction to Machine Learning"Mattingly "AI & Prompt Design" - Introduction to Machine Learning"
Mattingly "AI & Prompt Design" - Introduction to Machine Learning"
 
How to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseHow to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 Database
 
MS4 level being good citizen -imperative- (1) (1).pdf
MS4 level   being good citizen -imperative- (1) (1).pdfMS4 level   being good citizen -imperative- (1) (1).pdf
MS4 level being good citizen -imperative- (1) (1).pdf
 
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptxINCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
 
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
 
Comparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxComparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptx
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management System
 
Chi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical VariableChi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical Variable
 
Spearman's correlation,Formula,Advantages,
Spearman's correlation,Formula,Advantages,Spearman's correlation,Formula,Advantages,
Spearman's correlation,Formula,Advantages,
 
prashanth updated resume 2024 for Teaching Profession
prashanth updated resume 2024 for Teaching Professionprashanth updated resume 2024 for Teaching Profession
prashanth updated resume 2024 for Teaching Profession
 
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6
 

Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt

  • 1. K.V Faridkot Harkamalpreet Singh Brar 9 -B th
  • 3. Objectives  At the end of the lesson the students should be able; To find the surface area of a cylinder ..
  • 4. What is a cylinder?  The term Cylinder refers to a right circular cylinder. Like a right prism, its altitude is perpendicular to the bases and has an endpoint in each base.
  • 5. PRESENTATION base altitude radius base
  • 6. What will happen if we removed the end of the cylinder and unrolled the body? Lets find out !!!!
  • 7. This will happen if we unrolled and removed the end of a cylinder…. h Circumference of the base 2Πr 2
  • 8. Notice that we had formed 2 circles and a 1 rectangle….  The 2 circles serves as our bases of our cylinder and the rectangular region represent the body
  • 9. How can we solved the surface area of a Cylinder?  To solve the surface area of a cylinder, add the areas of the circular bases and the area of the rectangular region which is the body of the cylinder.
  • 10. This is the formula in order to solved the surface are of a cylinder.  SA= area of 2 circular bases + are of a rectangle oR
  • 11. We derived at this formula..!! SA=2Πr2 +2Πr Or SA=2Πr (r + h)
  • 12. Find the surface area of a cylindrical water tank given the height of 20m and the radius of 5m? (Use π as 3.14) Given: SA=2πr2 +2πrh h=20m r=5m =2(3.14)(5m)2 + 2[(3.14) (5m)(20m) =157m2 + 628m SA =785m2
  • 13. 2-Surface Area of a Prism Cubes and Cuboids
  • 14. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The top and the bottom of the cuboid have the same area.
  • 15. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The front and the back of the cuboid have the same area.
  • 16. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The left hand side and the right hand side of the cuboid have the same area.
  • 17. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. Can you work out the 5 cm 8 cm surface area of this cubiod? The area of the top = 8 × 5 = 40 cm2 7 cm The area of the front = 7 × 5 = 35 cm2 The area of the side = 7 × 8 = 56 cm2
  • 18. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. 5 cm So the total surface area = 8 cm 2 × 40 cm2 Top and bottom 7 cm + 2 × 35 cm2 Front and back + 2 × 56 cm2 Left and right side = 80 + 70 + 112 = 262 cm2
  • 19. Formula for the surface area of a cuboid We can find the formula for the surface area of a cuboid as follows. Surface area of a cuboid = w l 2 × lw Top and bottom h + 2 × hw Front and back + 2 × lh Left and right side = 2lw + 2hw + 2lh
  • 20. Surface area of a cube How can we find the surface area of a cube of length x? All six faces of a cube have the same area. The area of each face is x × x = x2 Therefore, x Surface area of a cube = 6x2
  • 21. Checkered cuboid problem This cuboid is made from alternate purple and green centimetre cubes. What is its surface area? Surface area =2×3×4+2×3×5+2×4×5 = 24 + 30 + 40 = 94 cm2 How much of the surface area is green? 48 cm2
  • 22. Surface area of a prism What is the surface area of this L-shaped prism? 3 cm To find the surface area of 3 cm this shape we need to add together the area of the two 4 cm L-shapes and the area of the 6 rectangles that make up 6 cm the surface of the shape. Total surface area = 2 × 22 + 18 + 9 + 12 + 6 + 6 + 15 5 cm = 110 cm2
  • 23. Using nets to find surface area It can be helpful to use the net of a 3-D shape to calculate its surface area. Here is the net of a 3 cm by 5 cm by 6 cm cubiod. 6 cm Write down the area of each 3 cm 18 cm2 3 cm 6 cm face. Then add the 5 cm 15 cm2 30 cm2 15 cm2 30 cm2 areas together to find the surface area. 3 cm 18 cm2 3 cm Surface Area = 126 cm2
  • 24. Using nets to find surface area Here is the net of a regular tetrahedron. What is its surface area? Area of each face = ½bh = ½ × 6 × 5.2 = 15.6 cm2 5.2 cm Surface area = 4 × 15.6 = 62.4 cm2 6 cm
  • 25. 3-Warm up: Finding the Area of a Lateral Face  Architecture. The lateral faces of the Pyramid Arena in Memphis, Tennessee, are covered with steal panels. Use the diagram of the arena to find the area of each lateral face of this regular pyramid.
  • 28. Surface Area of a Cone Unit 6, Day 4 Ms. Reed With slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of %20Pyramids%20and%20Cones%20C...
  • 29.  A cone has a circular base and a vertex that is not in the same plane as a base.  In a right cone, the height meets the base at its center. The vertex is directly Height above the center of the circle. Lateral Surface Slant Height r Base r  The height of a cone is the perpendicular distance between the vertex and the base.  The slant height of a cone is the distance between the vertex and a point on the base edge.
  • 30. Surface Area of a Cone  Surface Area = area of base + area of sector = area of base + π(radius of base)(slant height) S = B + π r l = π r + π rl 2 l B =πr 2 r
  • 31. Lateral Area of a Cone  Since Lateral Area = Surface Area – area of the base = π r + π rl L.A. = 2
  • 32. Example 1:  Find the surface area of the cone to the nearest whole number. a. 4 in. r = 4 slant height = 6 S = π r + π rl 2 = π (4) + π (4)(6) 2 6 in. = 16π + 24π = 40π = 40(3.14) ≈ 126in. 2
  • 33. Example 2:  Find the surface area of the cone to the nearest whole number. b. l 5 ft. 12 ft. First, find the slant height. Next, r = 12, l = 13. l =r +h 2 2 2 S = π r + π rl 2 = (12) + (5) 2 2 = π (12) + π (12)(13) 2 = 144 + 25 = 169 = 144π + 156π = 300π l = 169 = 13 ≈ 942 ft. 2
  • 34. On your own #1 Calculate the surface area of: S = π r 2 + π rl •S = π(7)2 + π(7)(11.40) •S = 49π + 79.80π •S = 128.8π
  • 35. On your own #2 Calculate the lateral area of: S = π r = π rl L.A. + 2 •L.A. = π(5)(13) •L.A. = 65π
  • 37. 4-Surface Area of a Sphere
  • 41.
  • 42.
  • 43. (Surface Area of a Sphere) = 4πr2
  • 44. 5-Basic Geometric Properties Volume of a cuboid
  • 45. In this lesson you will learn to calculate the volume of a cuboid
  • 47. Look at this cuboid Now imagine it is full of cubic centimetres 6 cm 1 cm3 4 cm 10 cm Can you see that there are 10 × 4 = 40 cubic centimetres on the bottom layer? There are 6 layers of 40 cubes making 40 × 6 = 240 cm3
  • 48. Let us go back and look at what we did here 6 cm height 4 cm breadth 10 cm length When we worked out the volume we multiplied the length by the breadth and then by the height Volume of a cuboid = length × breadth × height or V=lbh
  • 49. Lets us look again at the same cuboid and this 6 cm time try the formula 4 cm 10 cm V=lbh = 10 × 4 × 6 cm3 = 240 cm3 You will see that this is the same answer as we got before
  • 50. 6-Volume of a Cylinder
  • 51. What is Volume?  The volume of a three-dimensional figure is the amount of space within it.  Measured in Units Cubed (e.g. cm3)
  • 52. Volume of a Prism  Volume of a Prism is calculated by Volume = Area of cross section x perpendicular height V = Ah V = (4 x 4) x 4 = 64 m3
  • 53. What is this?  It has 2 equal shapes at the base, but it is not a prism as it has rounded sides It is a Cylinder
  • 54. Volume of a Cylinder  How might we find the Volume of a Cylinder?
  • 56. Pieces Missing  Find the volume of concrete used to make this pipe  Volume of Concrete = Volume of Big Cylinder – Volume of Small Cylinder (hole)
  • 57.  What shape is present here?
  • 58.  What 3D shapes can you see?
  • 59. HOME WORK Find the Volume of the Solid. To 1 decimal place
  • 61. Volume of a Cylinder  How might we find the Volume of a Cylinder?  V = Ah –=
  • 62. Conversion of units  1cm – 10mm  1m – 100cm  1km – 1000m
  • 63. Conversions of Units 1 cm2 = 10 mm x 10 mm =100 mm2 1 m2 = 100 cm x 100 cm = 10 000 cm2 1 m2 = 1000 mm x 1000 mm = 1 000 000 mm2 1 ha = 100 m x 100 m = 10 000 m2 1 km2 = 100 ha
  • 64. What about when cubic units?  1 cm3  = 1cm x 1cm x 1cm  = 10 mm × 10 mm × 10 mm  = 1000 mm3  1 m3  = 1m x 1m x 1m  = 100 cm × 100 cm × 100 cm  = 1 000 000 cm3
  • 65. Capacity  Volume - The volume of a three-dimensional figure is the amount of space within it.  Measured in Units Cubed (e.g. cm3)  Volume and capacity are related.  Capacity is the amount of material (usually liquid) that a container can hold.  Capacity is measured in millilitres, litres and kilolitres.
  • 67. How does Volume relate to Capacity?  1000 mL = 1 L  1000 L = 1 kL  1 cm3 = 1 mL  1,000cm3 = 1000ml = 1L  1 m3 = 1000 L = 1 kL
  • 68. Examples  Convert 1800 mL to L  1800ml = 1800/1000 = 1.8L  2.3 m3 to L 1m3 = 1000L (1kL)  2.3m3 = 2.3kL = 2300L
  • 69. Length = 5.53cm Capacity  Find the Capacity of this cube  Length = 5.53cm  V = Ah  = (5.53 x 5.53) x 5.53  = 169.11cm3 (1cm3 = 1ml)  Capacity = 169.11ml
  • 70. Example  Find the capacity of this rectangular prism.  Solution  Volume = Ah  = (26 x 12) x5  = 312 × 5  = 1560 cm3 (1cm3 = 1mL)  Capacity = 1560 mL or 1.56 L (1000mL = 1L)
  • 71. Ex 11.08 – Q 7.
  • 72.  What size rainwater tank would be needed to hold the run-off when 40 mm of rain falls on a roof 12 m long and 3.6 m wide? (Answer in litres.)
  • 74. Volume of Cylinders  Volume = Base x height  V = Bh B  Base area = π r2 r h
  • 75. Compare Cone and Cylinder  Use plastic space figures.  Fill cone with water.  Pour water into cylinder.  Repeat until cylinder is full. r r h
  • 76. Volume of Cone? =  3 cones fill the cylinder, so…  Volume = ⅓ Base x height
  • 77. Volume of Cone  3 cones fill the cylinder  Volume = ⅓ Base x height  V = ⅓ Bh h = 7 cm  Base area = π r2  V = ⅓ (π . 2.5 2) . 7 r =2.5 cm  V = ⅓ 3.14 . 6.25 . 7
  • 78. 8-Developing the Formula for the Volume of a Sphere
  • 79. Volume of a Sphere Using relational solids and pouring material we noted that the volume of a cone is the same as the volume of a hemisphere (with corresponding dimensions) Using “math language” Volume (cone) = ½ Volume (sphere) Therefore 2(Volume (cone)) = Volume (sphere) OR = +
  • 80. Volume of a Sphere We already know the formula for the volume of a cone. Volumecylinder Volumecone = 3 OR = ÷3
  • 81. Volume of a Sphere AND we know the formula for the volume of a cylinder Volumecylinder = ( Area of Base ) X (Height ) Height BASE
  • 82. Volume of a Sphere SUMMARIZING: Volume (cylinder) = (Area Base) (height) Volume (cone) = Volume (cylinder) /3 = ÷3 Volume (cone) = (Area Base) (height)/3 AND 2(Volume (cone)) = Volume (sphere) 2X =
  • 83. Volume of a Sphere 2(Volume (cone)) = Volume (sphere) 2X = 2(Area of Base) (height) /3= Volume (sphere) 2( πr2)(h)/3= Volume (sphere) r BUT h = 2r h r 2(πr )(2r)/3 = Volume(sphere) 2 4(πr3)/3 = Volume(sphere)
  • 84. 3 4π r  Volume of a Sphere 4 π r 3 3 3 3 4π r  Volumesphere = 3 4 π r 3 4 π r 3 3 3

Editor's Notes

  1. Discuss the meaning of surface area. The important thing to remember is that although surface area is found for three-dimensional shapes, surface area only has two dimensions. It is therefore measured in square units.
  2. Stress the importance to work systematically when finding the surface area to ensure that no faces have been left out. We can also work out the surface area of a cuboid by drawing its net ( see slide 51 ). This may be easier for some pupils because they would be able to see every face rather than visualizing it.
  3. Pupils should write this formula down.
  4. As pupils to use this formula to find the surface area of a cube of side length 5 cm. 6 × 5 2 = 6 × 25 = 150 cm 2 . Repeat for other numbers. As a more challenging question tell pupils that a cube has a surface area of 96 cm 2 . Ask them how we could work out its side length using inverse operations.
  5. Discuss how to work out the surface area that is green. Ask pupils how we could write the proportion of the surface area that is green as a fraction, as a decimal and as a percentage.
  6. Discuss ways to find the surface area of this solid. We could use a net of this prism to help find the area of each face.
  7. Links: S3 3-D shapes – nets S6 Construction and Loci – constructing nets