A chemical engineer designed a 625 ft long tailings channel to have a rhombus cross-section that is 9.5 ft deep, with walls sloping at an acute angle of 44„a.
A contractor placed a bid to excavate the canal at $195/cubic yard plus 20% profit. What was the bid?
To find the bid, we need to calculate the volume of the rhombus-shaped tailings channel and then multiply it by the excavation cost per cubic yard including the profit.
First, let's calculate the area of the rhombus-shaped cross-section. The formula for the area of a rhombus is:
Area = (diagonal1 * diagonal2) / 2
Since both diagonals of a rhombus bisect each other at right angles, we can use the formula:
Area = (side1 * side2) / 2
In this case, the diagonals of the rhombus are equal to the length and width of the cross-section, which is 625 ft.
Area = (625 ft * 625 ft) / 2
Area = 195,312.5 sq. ft
Next, we need to calculate the volume using the area and depth. The formula for the volume of a shape is:
Volume = Area * Depth
In this case, the depth is given as 9.5 ft.
Volume = 195,312.5 sq. ft * 9.5 ft
Volume = 1,857,968.75 cubic ft
Now, we need to convert the volume to cubic yards. Since 1 cubic yard is equal to 27 cubic feet, we divide the volume by 27.
Volume in cubic yards = 1,857,968.75 cubic ft / 27
Volume in cubic yards = 68,814.75 cubic yards
Next, we calculate the cost of excavation including profit. The excavation cost per cubic yard is given as $195, and the profit is 20% of the cost per cubic yard.
Profit = 20% * $195
Profit = $39
Total cost per cubic yard including profit = $195 + $39
Total cost per cubic yard = $234
Finally, we multiply the volume in cubic yards by the cost per cubic yard to find the bid:
Bid = Volume in cubic yards * Total cost per cubic yard
Bid = 68,814.75 cubic yards * $234
Bid ≈ $16,099,017.5
Therefore, the bid for excavating the canal is approximately $16,099,017.5.