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Answer :
The conical pile resulting from the excavation has a volume of approximately 19.63 cubic meters. The excavated material is not enough to fill the shaft after the foundation is constructed
To find the dimensions of the conical pile resulting from the excavation, we need to consider the diameter and depth of the circular shaft.
Given:
Diameter of the circular shaft = 5 meters
Depth of the circular shaft = 3 meters
To calculate the dimensions of the conical pile, we can use the formula:
V = (1/3) * π * r^2 * h
where V is the volume of the conical pile, π is the mathematical constant pi (approximately 3.14159), r is the radius of the circular base of the pile, and h is the height of the conical pile.
First, let's find the radius of the circular shaft:
Radius = Diameter / 2 = 5 / 2 = 2.5 meters
Next, let's find the volume of the conical pile:
V = (1/3) * π * (2.5^2) * 3
V ≈ 19.63 cubic meters
So, the conical pile resulting from the excavation has a volume of approximately 19.63 cubic meters.
Now, let's determine if the excavated material is enough to fill the shaft after the foundation is constructed. For this, we need to calculate the volume of the shaft and compare it to the volume of the conical pile.
Volume of the shaft = π * r^2 * h
Volume of the shaft = π * (2.5^2) * 3
Volume of the shaft ≈ 58.91 cubic meters
Since the volume of the conical pile (19.63 cubic meters) is smaller than the volume of the shaft (58.91 cubic meters), the excavated material is not enough to fill the shaft after the foundation is constructed. Additional material would be needed to fill the remaining volume of the shaft.
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