Formulae & Measurement Units Class 9 Notes | EduRev

Class 9 : Formulae & Measurement Units Class 9 Notes | EduRev

The document Formulae & Measurement Units Class 9 Notes | EduRev is a part of Class 9 category.
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Length:

  • 1 Centimetre (cm) = 10 milimetre(mm)
  • 1 Decimetre(dm) = 10 Centimetre
  • 1 Metre = 10dm = 100 cm = 1000mm
  • 1 Decametre (dam) = 10m = 1000cm
  • 1 Hectometre (hm) = 10dam = 100m.
  • 1 kilomemetre (km) =1000m = 100dam = 10hm.
  • 1 Myriametre =10Kilometre

Area:

  • 1cm2 =1 cm X 1cm= 10 mm X 10mm = 100 mm2
  • 1dm2 =1 dm X 1dm=10 cm X 10 cm =100 cm2
  • 1m2 = 1 m X 1 m = 10 dm = 10 dm = 100 dm2
  • 1 dam2 or 1are = 1 dam X 1dam = 10m X 10m = 100 m2
  • 1hm2 = 1 hectare = 1hm X 1hm = 100 m X 100 m = 10000 m2 = 100 dm2
  • 1km2 = 1 km X 1 km = 10 hm X 10 hm = 100 hm2 or 100 hectare

Volume:

  • 1 cm= 1 ml = 1 cm X 1 cm X 1 cm = 10 mm X 10 mm X 10 mm = 1000 mm3
  • 1 Litre = 1000 ml =1000 cm3.
  • 1 m3 = 1 m X 1 m X 1 m = 100 cm X 100 cm X 100 cm = 10cm3 = 1000 litre = 1 kilolitre
  • 1 dm3 = 1000 cm3
  • 1m3 = 1000 dm3
  • 1 km3 = 109m3

 

Let there be cuboids of Length (l), Breadth (b), Height (h), Area (A) and Volume (V):-

 

If the length (l) of each edge, Area (A) and Volume (V) of a Cube:-

 

 

Radius (r), height (h), Area (A), and Volume (V) ;

  1. Lateral or Curved surface area= 2πrh = Product of Circumference of the circle and height
  2. Each Surface area = π r2
  3. Total surface area of Right Circular cylinder= (2πrh + 2πr2) = 2πr (h+r).
  4. Each Base surface area = π (R2-r2) {R= radius of outer cylinder, r=radius of inner cylinder).
  5. Lateral or Curved surface area of hollow cylinder= (External surface area) + (Internal surface area) = 2πRh + 2πrh = 2πh (R+r).
  6. Total surface area of hollow cylinder=2 π Rh+2 π rh=2 π ( R2-r2 ) = 2πh (R+r) + 2π(R+r) (R-r) = 2π (R+r) (h+R-r)
  7. Volume of the cylinder =Measure of the space occupied by the cylinder=Product of the area of each circular sheet and height= π r2h.
  8. Volume of a Hollow Cylinder = Exterior Volume –Interior Volume= π R2h- π r2h= π (R2-r2)h
  1. Units of Measurement of Area and Volume
  2. Surface Area and Volume of Cuboids
    1. Total surface area of the cuboids = 2( lb + bh + lh ).
    2. Lateral surface area of the cuboids= 2( l + b ) h,i.e. Product of (Perimeter of the base) and (Height).
    3. Diagonal of the cuboids= √l2+b2+h2 i.e. square root of ( l2+b2+h2 ).
    4. Length of all 12 edges of the cuboids= 4 (l+b+h).
    5. Volume of a cuboids (V) =lbh, i.e. Product of (Area of the base) and (Height)
    6. l = V / bh; b = V / lh; h = V / lb or height = Volume divide by area of the base
  3. Surface Area and Volume of a Cube
    1. Total surface area of the cube = 6l2
    2. Lateral surface area of the cube = 4l2
    3. Diagonal of the cube =√3 l i.e. cube roots of length.
    4. Length of all 12 edges of the cube = 12 l.
    5. Volume of a Cube (V) = l= (edge).
    6. Edge of a cube= Cube roots of cube i.e. Formulae & Measurement Units Class 9 Notes | EduRev
  4. Surface Area and Volumeof a Right Circular Cylinder
    • Radius: The radius (r) of the circular base is called the radius of the cylinder.

       

    • Height: The length of the axis of the cylinder is called the height (h) of the cylinder.

       

    • Lateral Surface: The curved surface joining the two base of a right circular cylinder is called Lateral Surface.

       

    • Hollow Cylinder: A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.
  5. Surface Area and Volume of a Right Circular Cone

     

    • Base: a right circular cone has a plane end, which is in circular shape. This is called the base (π r2) of the cone.

       

    • Height: The length of the line segment joining the vertex to the centre of base is called the height (h) of the cone.

       

    • Slant Height: The length of the segment joining the vertex to any point on the circular edge of the base is called the slant height (l) of the cone.

       

    • Radius: The radius of the base circle is called the radius (r) of the cone.

       

    • The curved surface area of a cone is also called the lateral surface area.

    A Hollow Right Circular Cone of radius (r), height (h) and slant height (l), Area (A), Volume (V) then:

    1. Length of the circular edge=2 π r
    2. Area of the plane = π r2
    3. Curved surface area of the cone= Area of the Sector
      = 1|2 X (arc length) x ( radius)
      =1|2 x 2πr x l = πrl.
      = Half and (product of circumference of base) and (slant height)
    4. Total surface area of the cone =Curved surface area + Area of the base. = π rl+ π r2= π r (l+r).
    5. Volumes of a Right Circular Cone = 3 (Volume of the cone of radius r and height) = π r2h=1/3 (π r2) X h= 1/3 X (Area of the base) X (height).
  6. Surface Area and Volume of a Sphere/ Hemisphere

     

    • Sphere: A sphere can also be considered as a solid obtained on rotating a circle About its diameter.

       

    • Hemisphere: A plane through the centre of the sphere divides the sphere into two equal parts, each of which is called a hemisphere.

       

    • Spherical Shell: The difference of two solid concentric spheres is called a spherical shell.

       

    • A spherical shell has a finite thickness, which is the difference of the radii of the two solid spheres which determine it.

    Sphere is the radius r, Area (A) and Volume (V);

    1. Surface areas of a sphere: S = 4 π r2.
    2. Curved surface area of a hemisphere: S = 2 π r2.
    3. Total surface area of a hemisphere: S = 2 π r2+ π r2=3 π r2
    4. If ‘R’ and ‘r’ are outer and inner radii of a hemisphere shell, then Outer surface area = 4 π R2
    5. Volume of a sphere V = 4/3 X (π r3).
    6. Volume of a hemisphere V = 2/3 X (π r3).
    7. Volume of the spherical shell whose outer and inner radii and ‘R’ and ‘r’ respectively, V = 4/3 π(R3-r3)
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