8. Volume

Volume. The ordinary rules of mensuration are all that are needed to compute the volume of any excavation. The work is very simple when the area to be removed is regular; but when the outlines are very irregular and broken, . the easiest method to calculate the excavation is to divide the plan into geometrical figures which are easy to compute, and calculate the area of each one separately. These areas being added, and their sum multiplied by the depth of the cellar, will give the volume of the excavation.

Fig. 1.

An illustration of this method is shown in Fig. 1, which represents the plan of an irregular foundation. To compute the area of the excavation, the plan is divided into the rectangles a d c b, I k b m, j i h g, g f e c, and the polygons n q p o, t u rs , and a x w v. By scaling on the drawing the dimensions of these figures, the area of each may then be readily determined by calculation.

It is sometimes required to find the volume of an excavation, the surface of which is very irregular, as in Fig. 2; in such a case the following method may be used: Divide the surface of the excavation into a number of squares or rectangles, as at d e f c; these represent the ends of prisms, the other ends of which are the bottom of the excavation, as at a h g b. Then calculate the volume of each prism by ascertaining the height of the four corners above the bottom; add these measurements together, divide the sum by 4 (the number of corners), and multiply the result by the end area, as a h g b; the product will be the volume of the prism. The sum of these partial volumes will be an accurate estimate of the contents of the excavation.

Fig. 2.