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The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Using the given values, the volume of the cone-shaped container can be calculated as V = (1/3)(3.14)(4^2)(12) = (1/3)(3.14)(16)(12) ≈ 201.06 cubic feet.
Therefore, the container can store approximately 201.06 cubic feet of animal feed.