Surveying ME - BMEEOAFM201

Another method is based upon cross-sections. You have to calculate the area of each cross-section and the volume between two consecutive sections is their distance multiplied by the average of their areas.

Let's have two sections, their areas are $A_1$ and $A_2$ and the distance between them is $d_1$. This case the volume between the two sections is

$V_1= d_1\frac{A_1+A_2}{2}$

In general when you have $N$ sections:

$V=V_1+V_2+...+V_{N-1}=d_1 \frac{A_1+A_2}{2} +d_2 \frac{A_2+A_3}{2} +...+d_{N-1} \frac{A_{N-1}+A_N}{2}$

In the special case when $d_1=d_2=...=d_{N-1}=d$ the volume is:

$V= \frac{d}{2} (A_1+A_N+2(A_2+A_3+...+A_{N-1}))$