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Areas and Volumes - Coggle Diagram

- - - - Uses grids and counting square
    - - Trapezoidal Rule
        
        A=L(O1+2ΣO(From 2 to (n-1))+On)/2
      - Simpson's Rule
        
        A=L(O1+4ΣO(even no. from 2 to (n-1)) +2ΣO(odd no. from 3 to (n-1))+On)/2
        
        Better approximation than trapezoidal rule
        
        In case there is even number of offset, we can use Simpson's rule to calculate until the last odd offset, then continue by trapezoidal rule
    - - Planimeter
        
        It is a mechanical instrument to calculate the irregular area from a plan or map
  - - - Level across
      - 2-level section
      - 3-level section
      - Part cut part full
- - - - by using cell
      - Vtotal=Σ(h) used once+2Σ(h) used twice +3Σ(h) used thrice+4Σ(h) used 4 times
    - - Suitable for large volume
      - Can use both End Area or Prismoidal Method
    - - End Area Method
        
        V=L(A1+A2)/2
        
        Vtotal=L(A1+2ΣA(from 2 to (n-1))+An)/2
      - Prismoidal Method
        
        V=L(A1+4A2+A3)/3
        
        Vtotal=L(A1+4ΣA(even no. from 2 to n) +2ΣO(odd no. from 3 to n+An)/2 , n must be odd number