Cylinder,Sphere and cone
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Cylinder,Sphere and cone

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Volume ,surface area and exercise about Cylinder,Sphere and cone

Volume ,surface area and exercise about Cylinder,Sphere and cone

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Cylinder,Sphere and cone Cylinder,Sphere and cone Presentation Transcript

  • Volume and Surface Are of Cylinder, Sphere, and Cone
  • Cone
    +
    +
    =
    A Coneis a three dimensional solid with a circular base and a curved surface that gradually narrows to a vertex.
  • FORMULAS of a cone
    Surface Area : Area of base + lateral surface face
    : ∏r2 + ∏rs
    : ∏r (r + s)
    Lateral Surface Area : ∏rs
    Volume of a cone :
  • 1. Find the Volume of Cone
    Find the volume of a cone with a radius diameter=7cmand height=10cm, taking p=22/7
    Radius = 3.5 cm
    Volume of a Cone
    = (1/3) pr2h
    = (1/3)(22/7)(3.5)2(10)
    = 11 x 3.5 x 10
    Volume= 385cm3
  • 2. Find the lateral surface area
    The radius of cone’s base is 3cm and the height of the cone is 4cm, taking p = 3.14.
  • Answer:
    Lateral Surface Area = prs (slant height).
    S2 = r2 + t2 The lateral surface area = prs
    = 32 + 42 = 3.14 x 3 x 5
    = 9 + 16 = 47.1 cm2
    S2 = √25
    S = 5cm
  • Find the Surface Area of a Cone
    Find the area of a cone with a radius r=3 m and height h=4 m.
    r = the radius h = the height l = the slant height
    Use thePythagorean Theorem to find l
    l 2 = r2 + h2
    l 2= (3)2 + (4)2
    l 2= 25
    l = 5
    Total Surface Area of a Cone
    = pr2 + Lateral surface area
    = pr2 + prs
    = 3.14(3)2 + 3.14(3)(5)
    = 75.36 m2
  • Volume of sphere
    r
    h
    r
    Volume of a Sphere = 2 x (2 x volume of a cone)
    = 4 x 1/3∏r2t  substitute t = r
    = 4 x 1/3 ∏r2 x r
    Volume of a Sphere = 4/3 ∏r3
  • Question for volume of a sphere
    9
    The radius of a sphere is 7 cm. Find the volume of the sphere if we have ∏=22/7!
    V= 4/3 ∏r3
    V= 4/3. 22/7. 73
    V= 1473
    Thus, the volume of the sphere is 1473 cm3.
  • Volume of a Cylinder = base x height = pr2h
    = 3.14(1)2(2)
    = 6.28 m3
  • Volume of a cylinder
    Find the volume of a cylinder with a radius r=1 m and height h=2 m.
    Know : r = 1 m h = 2 m
    Ask : Volume?
    Answer : V = ∏r2t
    V = 3.14 X 1 X 1 X 2
    V = 6.28cm3
  • FORMULAS OF CYLINDER
    Lateral Surface Area :Circumference of the base x height of the cylinder’
    Total Surface Area :2∏r ( r +t )
  • Question for surface area of a cylinder
    The height of a cylinder is 15 cm. And the radius is 14cm. Find the surface area of the cylinder.
    Answer:
    2 ∏r(r + t)
    2 x 22/7 x 14 x (14 + 15)
    88 x 29 = 2552 cm2