Final answer:
The volume of the cone-shaped pile of sand is approximately 367.53 cubic feet.
Step-by-step explanation:
The volume of the cone-shaped pile of sand can be calculated using the formula \(V = \frac{1}{3}\pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the altitude. In this case, the radius is 5 feet and the altitude is 11 feet 2 inches. To convert the altitude to feet, we can use the fact that 1 foot is equal to 12 inches. So the altitude in feet is \(11 + \frac{2}{12} = 11.166\) feet. Now we can plug in the values into the formula: \[V = \frac{1}{3} \times 3.14 \times 5^2 \times 11.166 \approx 367.53 \text{ cubic feet}\]