Measurements for volume are nothing more than applying basic distance and height measurements to where the volume is to be determined. It is usually not practical to take the time to collect data everywhere where there is little variation in altitude. Therefore, it should be understood that the calculation of quantities does not give an accurate answer. Usually, approximations should be made and the average determined. The field engineer will analyze the data and make decisions that result in the best estimation of the volume.

Table of Contents

## 1. Area

The key to volume calculation is the determination of the area. Most volume calculation formulas have a formula for an area within them, which is then multiplied by the height to determine the volume. For example, the area of a circle is pi times the square of the radius. The volume of a cylinder is the area of the circle times the height of the cylinder. If an area can be determined, it is generally easier to determine the quantity.

## 2. counting the squares

Approximation is possible by plotting the figure on a scale on cross-sectional paper and counting the squares. each class represents *x *Number of square feet. Incomplete sections are visually combined and averaged along the edges of the cross section.

## 3. planimeter

Electromechanical digital planimeter is a quick way to determine the area of irregularly shaped figures. The irregular shape is drawn on a scale and a planimeter is used to trace the outline of the shape. Entering the scale factor into the planimeter gives a digital readout of the area.

## 4. geometric formula

Although a shape may seem irregular at first, it is often possible to break it down into smaller regular shapes such as squares, rectangles, triangles, trapezoids, etc., which would allow the use of standard geometric formulas to determine the area. This method can be cumbersome because of all the shapes required for the calculations.

## 5. cross-section coordinates

If cross-sectional field data is available, using this data is the recommended method of calculating volume. Once understood, this procedure is the fastest and most accurate way to determine area. Cross-section data collected on a project represents elevation and location information for points on the ground. These points can be used as coordinates to determine the area.

The roadway employed in road construction would require changing the shape of the land to overcome the fluctuations of hills and valleys. Often mountains of dirt must be moved to create a gentle grade for the road. Payment for dirt removal and application is usually on a unit cost basis. That is, the contractor will be paid per cubic yard of soil and will receive a separate price per cubic yard of rock.

It can be seen that accurate determination of the quantity transferred is important for the owner and the contractor. Everyone wants an exact quantity so the pay for the work is accurate.

For road projects, the cross section of the ground height is measured at the beginning of the project, during the project and at the end of the project. The comparison between the final cross section and the original cross section is used to determine the volume transferred. The areas of cross sections are easily determined using the heights of the points from the center line (coordinates) and their locations.

**average end zone method** Uses and averages the end zones of stations along the route. refer to **Figure 1**, Then this average is multiplied by the distance between the two end regions to get the volume between them. The process in formulaic form is as follows:

**Volume = [L/27],[(Area 1 + Area 2)/2]**

where **Took** Represents the distance between the cross-sectional end areas being used in the formula, and 27 represents the number of cubic feet in 1 cubic yard. Cubic feet divided by 27 converts to cubic yards.

a method known as ** credit pit leveling** Can be used effectively to determine quantity on construction projects.

A grid is established by the field engineer and the height at the grid points is determined both before the excavation begins and upon completion of the work.

The lend-pit method uses a grid and the average depth of the excavation to determine the volume. Before the start of the excavation, the field engineer creates a grid over the entire area where the excavation is to take place. Elevation data is collected at each grid point and recorded for future reference. At any time during the excavation, the field engineer may re-establish the grid and set a new height for each field point. Using the average height formula shown below, the amount of soil removed from each grid area can be determined. refer to **line drawing number 2**, The smaller the grid interval, the more accurate the volume.

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