A vase maker decides to construct a vase whose contour is a cubic polynomial according to the following specifications:
The vase is 4 feet tall.
The vase is 4 feet in diameter at its widest (which occurs 1 foot from the base).
The vase is 2 feet in diameter at its narrowest (which occurs 1 foot from the top).
The vase has a flat circular bottom.
Rounded to 3 decimal places, what is the volume of the vase in cubic feet?