To find the weight of the pile of gravel, we first need to calculate its volume using the formula for the volume of a cone.
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
- Find the radius: The base diameter is 10 feet, so the radius \( r \) is:
\[ r = \frac{10}{2} = 5 \text{ feet} \]
-
Height: The height \( h \) is given as 4 feet.
-
Substitute values into the volume formula:
\[ V = \frac{1}{3} \pi (5^2) (4) \]
Calculating \( 5^2 \):
\[ 5^2 = 25 \]
Now substitute back into the volume formula:
\[ V = \frac{1}{3} \pi (25) (4) = \frac{100}{3} \pi \]
- Approximate the value of \(\pi\), using \( \pi \approx 3.14 \):
\[
V \approx \frac{100}{3} \times 3.14 \approx \frac{314}{3} \approx 104.67 \text{ cubic feet}
\]
- Weight of gravel: Since 1 cubic foot of gravel weighs 30 pounds, the total weight \( W \) of the gravel is given by:
\[ W = V \times 30 \]
Substituting the volume we found:
\[ W \approx 104.67 \times 30 \approx 3140.1 \text{ pounds} \]
Rounding this to the nearest pound gives approximately:
\[ W \approx 3140 \text{ pounds} \]
However, let’s confirm our calculations by directly multiplying:
\[ 104.67 \times 30 = 3140.1 \text{ pounds} \]
Thus, the final weight of the pile of gravel, rounded to the nearest pound, is approximately:
\[ \text{Weight of the pile of gravel} = \boxed{3140} \text{ pounds} \]
It appears that none of the provided options (3,142 pounds, 9,425 pounds, 12,566 pounds, 15,708 pounds) match this calculated value. Please ensure the question and options provided are accurate.