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 