The ditch's wedge sectors are assumed to be the same size in order to simplify calculations. The total volume of the wedge was calculated using the formula for a triangular prism and assigned the variable [L]: [L] = Volume of total sector = (1/2) * B * H * W. From this, both the volume of the pyramid from the narrower end of the wedge and the volume of the slope at the other end of the wedge were subtracted.
B  width of the top of the slope
H  total length of the sector
W  height of the slope
The volume of the pyramid, [M], was calculated using (1/3) * S * y * W where W is the height of the pyramid, y is the length of the pyramid< along the bottom of the trench, and S is length of the pyramid along the outside edge.
The volume of the slope, [N], was calculated using (1/2) * x * W * B  2[(1/3) * z * x * W], where x is the length of the base of the slope, W is the height of the slope, B is the width of the top of the slope, z is the difference between B and the width at the base of the slope.

Minimum Estimate 
Maximum Estimate 
B 
6 
7 
H 
9 
10.3 
W 
4.8 
5 
S 
3.4 
4.1 
Y 
3.1 
4.2 
X 
3 
4 
Z 
1.6 
0.9 
[L] 
129.6 
180.25 
[M] 
16.864 
28.7 
[N] 
27.84 
58 
Dirt removed per sector 
84.896 
93.55 
Total Dirt Removed 
848.96 
935.5 