# Ditch Wedge

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