Calculation Of Area & Volume

Area calculation from plans

Calculating cross-sectional areas

Volume estimation

Irregular boundaries

Combination of regular & irregular

Regular boundaries

Area can be calculated using formulas for triangle or coordinates Capture2

Area from coordinates Capture1

Mathematics

Mechanical

Graphical

‐Uses grids and counting squares

Trapezoidal

Planimeter : mechanical instrument specifilcally designed to calculate irregular areas from plans and maps.

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If there are n offsets Capture 4

Simpson

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For n offsets Capture6

Trapezoidal vs Simpson

Simpson approximate boundaries as curve sections

Preference should be given to Simpson. In cases where offsets are even numbers, partly calculate using Simpson (up to odd offsets) and trapezoidal for the remaining offsets

therefore better approximation than trapezoidal

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the reduced levels of these
points are determined determined using any suitable suitable method

reduced levels of points that lie to the left and right of the centre line at right angle are also observed, thus, creating cross‐sections

Setting‐out of roads, highways, railway track, etc., are normally done at regular intervals along the centre line

Cross Sections
& Longitudinal Sections

LONGITUDINAL SECTION

CROSS SECTION

Reduced level of the centre‐line observed produced longitudinal sections

Determine the
vertical curve

Observations of reduced levels at point that lie at right angle of the centre‐line produced cross‐sections

Calculated by

Mathematical formula (software)

Grid & Counting Squares (manual)

Planimeter (manual – easy)

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11

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Spot heights

Contours

Cross‐sections

End‐Areas

Prismoidal

Example ‐ cutting and filling of earth for basement (car park), underground water tanks, to obtain required formation levels, etc

A grid is f d orme over the area, and the reduce levels
of the grid points are determined

Used in ‘localised’ construction, such as earthwork for
the construction of buildings.

The difference between the grid heights and the proposed heights are obtained in order to estimate volumes

Suitable to be used when large volume is involved, such as, volumes of water contained in a dam, soil such as, volumes of water contained in a dam, soil

The area of a contour contour surface surface is determined determined. The contour’s surface can be treated as a cross‐section whose areas can be calculated either graphically or mechanically

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