To find the volume of a cone-shaped container, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
In this case, the radius \( r \) is 4 feet and the height \( h \) is 12 feet. Plugging the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (4^2) \times 12 \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now substitute back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 16 \times 12 \]
Now calculate \( 16 \times 12 \):
\[ 16 \times 12 = 192 \]
Now substitute again into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 192 \]
Now, calculate \( 3.14 \times 192 \):
\[ 3.14 \times 192 = 602.88 \]
Finally, we need to divide by 3:
\[ V = \frac{602.88}{3} = 200.96 \]
Therefore, the volume of feed that the container can store is approximately:
\[ \boxed{200.96} \text{ cubic feet} \]