Revision Notes of Chapter 13 Surface Areas and Volumes Class 9th Math

Topics in the Chapter
  • Basic Revision
  • Formula for Cuboid
  • Formula for Cube
  • Formula for Right Circular Cylinder
  • Formula for Right Circular Cone
  • Formula for Sphere
  • Formula for Hemisphere
  • Tips and Notes
    Basics Revision
    • The bodies occupying space are called solids, such as a cuboid, a cube, a cylinder, a cone, a sphere, etc. These solids have plane or curved surfaces.
    • The outer surface of a cuboid is made up of six rectangles. If we take the length of the cuboid as ℓ, breadth as b and the height as h, then Surface area of a cuboid = 2[lb + bh + hl]
    • The cuboid whose length, breadth and height are equal is called a cube. Let each edge of the cube be ‘a’, then Surface area of a cube = 6a2
    Formula for Cuboid
    Curved Surface Area for Cuboid or Area of four walls = 2(bh + hl)  = 2(l + b) × h 
    Total Surface Area for Cuboid = 2(lb + bh + hl)
    Volume for Cuboid = l×b×h

    Formula for Cube
    Curved Surface Area for Cube or Area of four walls = 4l2 
    Total Surface Area for Cube = 6l2 
    Volume for Cube = l3

    Formula for Right Circular Cylinder
    Curved Surface Area for Right Circular Cylinder = 2πrh  
    Total Surface Area for Right Circular Cylinder = 2πr(r + h) 
    Volume for Right Circular Cylinder = πr2h

    Formula for Right Circular Cone
    Slant height of right Circular Cone: 
    Curved Surface Area for Right Circular Cone = πrl  
    Total Surface Area for Right Circular Cone = πr(r + l) 
    Volume for Right Circular Cone = 1/3 (πr2h) 

    Formula for Sphere
    Curved Surface Area for Sphere = 2πrh  
    Total Surface Area for Sphere = 2πr(r + h) 
    Volume for Sphere = πr2h

    Formula for Hemisphere
    Curved Surface Area for Hemiphere = 4πr2   
    Total Surface Area for Hemiphere = 4πr2
    Volume for Hemiphere = 4/3(πr3)

    Tips and Notes

    • Area × Rate = Cost
    • Density = Mass/Volume
    • 1 m3 = 1000 litres
    • 1 L = 1000 cm2
    • Speed = Distance/Time
    • 1 km = 1000 m = 105 cm
    • 1 km2 = 106 m2
    • 1 m = 100 cm
    • 1 m2 = 10000 cm2
    • 1 km/hr = 5/18 m/sec
    • 1 km/hr = 50/3 m/min
    • Shape of the river = cuboid 
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