Given the end areas below, calculate the volumes of cut (in cubic meters) and fill between stations 0+00 and 1+50. Determine the true amount of excess cut or fill to be removed.
0+00: Fill = 60
0+50: Fill = 50
0+75: Cut = 0, Fill = 25
1+00: Cut = 10, Fill = 5
1+15: Cut = 15, Fill = 0
1+50: Cut = 30
Two different methods need to be used here to compute earthwork volumes along the five strips. The average end area method can be used for non-zero sections. The pyramid method needs to be used for areas with zero ends.
For 0+00 to 0+50, use average end area:
For 0+50 to 0+75, use average end area:
For 0+75 to 1+00, use the average end area method for the fill section and the pyramid method for the cut section:
For 1+00 to 1+15, use the pyramid method for the fill section and the average end area method for the cut section:
For 1+15 to 1+50, use the average end area method:
The sums of both cut and fill can be found:
Fill = 4087.5 cubic-meters
Cut = 1058.3 cubic-meters
Thus, 3029.2 cubic-meters of dirt are needed to meet the earthwork requirement for this project.