Final answer:
The volume of the conical spoil pile is 2007.2 ft^3
Step-by-step explanation:
To find the volume of the conical spoil pile, we can use the formula for the volume of a cone: V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. Since we have the diameter of the base, we can divide it by 2 to get the radius. The height can be found using trigonometry. We can use the angle of repose to find the height as h = r * tan(angle).
In this case, the radius of the base is 16.5 ft (33 ft divided by 2) and the angle of repose is 34 degrees. Plugging these values into the formulas, we get:
V = (1/3) * 3.14 * (16.5 ft)^2 * (16.5 ft * tan(34 degrees)) = 2007.2 ft^3.
Since the volume is measured in cubic feet, we don't need to convert it to lcy (loose cubic yards). Therefore, the volume of the pile is 2007.2 ft^3.
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