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Lecture_16_-_Areas_and_Volumes.ppt

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Lecture_16_-_Areas_and_Volumes.ppt Powered By Docstoc
					Faculty of Applied Engineering and
          Urban Planning
  Civil Engineering Department




              Surveying
                    First Semester
                       2011/2012


        Areas and Volumes
                  Lecture 16 - Week 10
Content

  1. Introduction to Areas and Volumes
  2. Regular Figures
  3. Irregular Figures
Planimeters




 Digital Planimeter   Optical Polar Planimeter
Planimeters
Areas
  1. Regular Figures
        •   Mathematical Formulae
        •   Method of Coordinates
  2. Irregular Figures
        •   Graphical Method
        •   Give and Take Method
        •   Trapezoidal Rule
        •   Simpson’s One-Third Rule
Mathematical Formulae




1      1
  bh or a  b  sin(C)        a2                    ab
2      2




  1
    h  a  b          1               180     1
                           n  a 2  cot            π  d2
  2                      4               n        4
Mathematical Formulae




                                 1 2  π         
 
π r r
     2     2
                   1
                       πr 2
                                  r 
                                 2  180
                                           sin  
                                                  
     2    1
                   360




                      2
     πa  b           bh
                      3
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates
Areas by Method of Coordinates


 Area = 0.5(| 136840.01 – (-84890.94) |)
      = 110865.48 ft2
Areas

  Irregular Figures
        •   Give and Take Method
        •   Graphical Method
        •   Trapezoidal Rule
        •   Simpson’s One-Third Rule
Give and take Method

In this method, the irregular figure is replaced
by a regular one of approximately equal area
that can be calculated by one of the methods
explained earlier.
Graphical Method




                   =1 cm2
Trapezoidal Rule
Trapezoidal Rule
Trapezoidal Rule
Example
Example
 Simpson’s One-Third Rule




                   Offset



       Intercept


ONLY   used with Odd number of offsets
       (i.e. Even number of Intercepts)
Simspon’s One-Third Rule
Example
HW Mathematical Formulae




          20 m   15 m
Questions?!

				
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posted:10/7/2012
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