1. ADVANCE SURVEYING

2. Areas from cross-sections
Two-level section in filling

3. The same formula as derived above is applicable
The same formula as derived above is applicable. Hence if b, h, n, m are given h1, h2, w1 and w2 can be computed and the area obtained as shown above.

4. Side hill two-level section
From the geometry of Fig. below

5. From similar triangles HGF and FIC

7. Multilevel section
Figure below shows a multilevel section where more than three levels are required to define the transverse slope of the ground. For a multilevel section the coordinate method of determining area is convenient. This has already been explained before.

9. FORMULAE FOR COMPUTATION OF VOLUMES
1- Volume by average end areas
The volume by this method is given by
=Average end areas x Length between the sections
2- Prismoidal Formula
The volume is

10. Here Ao , A1 are the end areas where as M is the area of the middle section.
3- Volume by mean area method
In this method the mean cross sectional area of the various sections is first computed as
Volume V = Am X L where L is the length between the first and last section.

11. 4- Trapezoidal rule for computing volumes
If we have a series of sectional areas A1, A2……., Am at an equal interval of D, by end area methods

12. THANK YOU