As viewed from above, a swimming pool has the shape of the ellipse given by $$\frac{x^2}{1600}+\frac{y^2}{400}=1$$
The cross sections perpendicular to the ground and parallel to the $y$-axis are squares. Find the total volume of the pool. (Assume the units of length and area are feet and square feet respectively. Do not put units in your answer.)

$V$ = $\textrm{ft}^3$