Mathematics (4024)
Topic 7 of 8Cambridge O Levels

Mensuration

Area, perimeter, surface area and volume of 2D and 3D shapes

2D Shapes:

  • Rectangle: Area = l × w, Perimeter = 2(l + w)
  • Triangle: Area = ½ × base × height
  • Circle: Area = πr², Circumference = 2πr (or πd)
  • Trapezium: Area = ½(a + b) × h

    • 3D Shapes:

  • Cuboid: Volume = l × w × h, SA = 2(lw + lh + wh)
  • Cylinder: Volume = πr²h, Curved SA = 2πrh, Total SA = 2πr² + 2πrh
  • Cone: Volume = ⅓πr²h, Curved SA = πrl (l = slant height)
  • Sphere: Volume = ⁴⁄₃πr³, SA = 4πr²
  • Prism: Volume = cross-section area × length

    • Arc & sector: Arc length = (θ/360) × 2πr. Sector area = (θ/360) × πr².

    Key Points to Remember

    • 1Circle: A = πr², C = 2πr
    • 2Cylinder volume = πr²h
    • 3Sphere volume = 4/3 πr³
    • 4Sector area = (θ/360) × πr²

    Pakistan Example

    Water Tanks on Karachi Rooftops — Volume Calculations

    A typical Karachi rooftop water tank is a cylinder: radius 0.5m, height 1.2m. Volume = π(0.5)²(1.2) = 0.942 m³ ≈ 942 litres. Knowing this helps families calculate if their tank holds enough for a day's usage during water shortages.

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    Equations & InequalitiesTrigonometry & Bearings