K.V    FaridkotHarkamalpreetSingh 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 perpendi...
PRESENTATION          base          altitude        radius        base
What will happen if we removed the end of thecylinder and unrolled the          body?  Lets find out !!!!
This will happen if we unrolled  and removed the end of a          cylinder….                           h           Circum...
Notice that we had formed 2 circles and a 1 rectangle…. The 2 circles serves as our bases of  our cylinder and the rectan...
How can we solved the surface    area of a Cylinder? To solve the surface area of a  cylinder, add the areas of the  circ...
This is the formula in order to solved the surface are of a           cylinder. SA= area of 2 circular bases  + are of a ...
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...
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.            ...
Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces.            ...
Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces.            ...
Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces.            ...
Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces.            ...
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 cube   How can we find the surface area of a cube of length x?                          All six faces of...
Checkered cuboid problemThis cuboid is made from alternate purple and greencentimetre cubes.                             W...
Surface area of a prism          What is the surface area of this L-shaped prism?                3 cm                     ...
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...
Using nets to find surface area Here is the net of a regular tetrahedron.                    What is its surface area?    ...
3-Warm up: Finding the Area of aLateral Face Architecture. The lateral faces of the  Pyramid Arena in Memphis, Tennessee,...
Pyramid Arenamynameismr.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                                            ...
 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...
Surface Area of a Cone Surface Area = area of base + area of sector  = area of base + π(radius of base)(slant height)    ...
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 heigh...
Example 2: Find the surface area of the cone to the nearest whole  number.b.                               l             ...
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•...
On your own #2Calculate the lateral area of:   S   = π r = π rl          L.A. +             2  •L.A. = π(5)(13)  •L.A. = 65π
HomeworkWork 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 learnto calculate the volume of a           cuboid
Cuboids
Look at this cuboidNow imagine it is fullof cubic centimetres                                                             ...
Let us go back and look at what we did here                                                      6 cm                     ...
Lets us look againat the samecuboid and this                                                     6 cmtime try theformula  ...
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...
Volume of a Prism Volume of a Prism is calculated byVolume = Area of cross section x perpendicular height  V = Ah  V = (4...
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...
 What shape is present here?
 What 3D shapes can you see?
HOME WORKFind 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 Units1 cm2 = 10 mm x 10 mm      =100 mm21 m2   = 100 cm x 100 cm   = 10 000 cm21 m2   = 1000 mm x 1000 mm =...
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 c...
Capacity Volume - The volume of a three-dimensional  figure is the amount of space within it. Measured in Units Cubed (e...
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...
Examples Convert 1800 mL to L 1800ml = 1800/1000          = 1.8L 2.3 m3 to L            1m3 = 1000L  (1kL) 2.3m3 = 2.3...
Length = 5.53cm                Capacity Find the Capacity of this cube Length = 5.53cm V = Ah = (5.53 x 5.53) x 5.53 ...
Example Find the capacity of this rectangular prism. Solution Volume = Ah = (26 x 12) x5 = 312 × 5 = 1560 cm3       ...
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 wi...
7-Volume of Cones
Volume of Cylinders Volume = Base x height V = Bh                               B Base area = π r2                 r   ...
Compare Cone and Cylinder   Use plastic space figures.   Fill cone with water.   Pour water into cylinder.   Repeat un...
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 ar...
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 volu...
Volume of a SphereWe already know the formula for the volume of a cone.                                 Volumecylinder    ...
Volume of a SphereAND we know the formula for the volume of a cylinder        Volumecylinder = ( Area of Base ) X (Height ...
Volume of a SphereSUMMARIZING:Volume (cylinder) = (Area Base) (height)Volume (cone) = Volume (cylinder) /3              = ...
Volume of a Sphere       2(Volume (cone)) = Volume (sphere)      2X                 =2(Area of Base) (height) /3= Volume (...
34π r             Volume of a Sphere       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
Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt
Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt
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  • 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.
  • 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.
  • Pupils should write this formula down.
  • 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.
  • 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.
  • 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.
  • Links: S3 3-D shapes – nets S6 Construction and Loci – constructing nets
  • Surface area of a cuboid and a cube,cylinder,cone,sphere,volume of cuboid,cylinder,cone and sphere.ppt

    1. 1. K.V FaridkotHarkamalpreetSingh Brar 9 -B th
    2. 2. Topic
    3. 3. Objectives At the end of the lesson the students should be able; To find the surface area of a cylinder ..
    4. 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. 5. PRESENTATION base altitude radius base
    6. 6. What will happen if we removed the end of thecylinder and unrolled the body? Lets find out !!!!
    7. 7. This will happen if we unrolled and removed the end of a cylinder…. h Circumference of the base2Πr 2
    8. 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. 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. 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. 11. We derived at this formula..!!SA=2Πr2 +2Πr Or SA=2Πr (r + h)
    12. 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 +2πrhh=20mr=5m =2(3.14)(5m)2 + 2[(3.14) (5m)(20m) =157m2 + 628m SA =785m2
    13. 13. 2-Surface Area of a Prism Cubes and Cuboids
    14. 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. 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. 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. 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 cm27 cm The area of the front = 7 × 5 = 35 cm2 The area of the side = 7 × 8 = 56 cm2
    18. 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 bottom7 cm + 2 × 35 cm2 Front and back + 2 × 56 cm2 Left and right side = 80 + 70 + 112 = 262 cm2
    19. 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. 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. 21. Checkered cuboid problemThis cuboid is made from alternate purple and greencentimetre 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. 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 up6 cm the surface of the shape. Total surface area = 2 × 22 + 18 + 9 + 12 + 6 + 6 + 15 5 cm = 110 cm2
    23. 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 the5 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. 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. 25. 3-Warm up: Finding the Area of aLateral 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.
    26. 26. Pyramid Arenamynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
    27. 27. mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
    28. 28. Surface Area of a Cone Unit 6, Day 4 Ms. ReedWith slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of %20Pyramids%20and%20Cones%20C...
    29. 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. 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. 31. Lateral Area of a Cone Since Lateral Area = Surface Area – area of the base = π r + π rl L.A. = 2
    32. 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. 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 = 300πl = 169 = 13 ≈ 942 ft. 2
    34. 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. 35. On your own #2Calculate the lateral area of: S = π r = π rl L.A. + 2 •L.A. = π(5)(13) •L.A. = 65π
    36. 36. HomeworkWork Packet:Surface Area of Cones
    37. 37. 4-Surface Area of a Sphere
    38. 38. Sphere
    39. 39. Hemisphere
    40. 40. Great Circle
    41. 41. (Surface Area of a Sphere) = 4πr2
    42. 42. 5-Basic Geometric Properties Volume of a cuboid
    43. 43. In this lesson you will learnto calculate the volume of a cuboid
    44. 44. Cuboids
    45. 45. Look at this cuboidNow imagine it is fullof cubic centimetres 6 cm 1 cm3 4 cm 10 cmCan you see that there are 10 × 4 = 40 cubic centimetres on thebottom layer?There are 6 layers of 40 cubes making 40 × 6 = 240 cm3
    46. 46. Let us go back and look at what we did here 6 cm height 4 cm breadth 10 cm lengthWhen we worked out the volume we multiplied the length by thebreadth and then by the heightVolume of a cuboid = length × breadth × height or V=lbh
    47. 47. Lets us look againat the samecuboid and this 6 cmtime try theformula 4 cm 10 cm V=lbh = 10 × 4 × 6 cm3 = 240 cm3You will see that this is the same answer as we got before
    48. 48. 6-Volume of a Cylinder
    49. 49. What is Volume? The volume of a three-dimensional figure is the amount of space within it. Measured in Units Cubed (e.g. cm3)
    50. 50. Volume of a Prism Volume of a Prism is calculated byVolume = Area of cross section x perpendicular height V = Ah V = (4 x 4) x 4 = 64 m3
    51. 51. 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
    52. 52. Volume of a Cylinder How might we find the Volume of a Cylinder?
    53. 53. Example V = Ah
    54. 54. Pieces Missing Find the volume of concrete used to make this pipe Volume of Concrete = Volume of Big Cylinder – Volume of Small Cylinder (hole)
    55. 55.  What shape is present here?
    56. 56.  What 3D shapes can you see?
    57. 57. HOME WORKFind the Volume of the Solid. To 1 decimal place
    58. 58. Homework/Challenge Challenge Question
    59. 59. Volume of a Cylinder How might we find the Volume of a Cylinder? V = Ah –=
    60. 60. Conversion of units 1cm – 10mm 1m – 100cm 1km – 1000m
    61. 61. Conversions of Units1 cm2 = 10 mm x 10 mm =100 mm21 m2 = 100 cm x 100 cm = 10 000 cm21 m2 = 1000 mm x 1000 mm = 1 000 000 mm21 ha = 100 m x 100 m = 10 000 m21 km2 = 100 ha
    62. 62. 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
    63. 63. 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.
    64. 64. Examples of Capacity
    65. 65. 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
    66. 66. Examples Convert 1800 mL to L 1800ml = 1800/1000 = 1.8L 2.3 m3 to L 1m3 = 1000L (1kL) 2.3m3 = 2.3kL = 2300L
    67. 67. 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
    68. 68. 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)
    69. 69. Ex 11.08 – Q 7.
    70. 70.  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.)
    71. 71. 7-Volume of Cones
    72. 72. Volume of Cylinders Volume = Base x height V = Bh B Base area = π r2 r h
    73. 73. Compare Cone and Cylinder Use plastic space figures. Fill cone with water. Pour water into cylinder. Repeat until cylinder is full. r r h
    74. 74. Volume of Cone? = 3 cones fill the cylinder, so… Volume = ⅓ Base x height
    75. 75. 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
    76. 76. 8-Developing the Formula for the Volume of a Sphere
    77. 77. 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 = +
    78. 78. Volume of a SphereWe already know the formula for the volume of a cone. Volumecylinder Volumecone = 3 OR = ÷3
    79. 79. Volume of a SphereAND we know the formula for the volume of a cylinder Volumecylinder = ( Area of Base ) X (Height ) Height BASE
    80. 80. Volume of a SphereSUMMARIZING:Volume (cylinder) = (Area Base) (height)Volume (cone) = Volume (cylinder) /3 = ÷3Volume (cone) = (Area Base) (height)/3AND 2(Volume (cone)) = Volume (sphere) 2X =
    81. 81. 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)
    82. 82. 34π r  Volume of a Sphere 4 π r 3 3 3 3 4π r  Volumesphere = 34 π r 3 4 π r 3 3 3

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