The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- Radius \( r = 4 \) feet
- Height \( h = 12 \) feet
We can substitute these values into the formula:
\[ V = \frac{1}{3} \pi (4^2)(12) \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now substitute that back into the volume formula:
\[ V = \frac{1}{3} \pi (16)(12) \]
Now, multiply \( 16 \) by \( 12 \):
\[ 16 \times 12 = 192 \]
So now we have:
\[ V = \frac{1}{3} \pi (192) = \frac{192}{3} \pi = 64 \pi \]
To find the approximate numerical value, we can use \( \pi \approx 3.14 \):
\[ V \approx 64 \times 3.14 \approx 200.96 \]
Thus, the volume of the cone-shaped container is approximately:
\[ V \approx 200.96 \text{ cubic feet} \]
In summary, the volume of feed this container can store is \( 64\pi \) cubic feet, or approximately 200.96 cubic feet.
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