Metal spheres, each of radius \( 2\ cm\), are packed into a rectangular box of internal dimensions \(16 cm \times 13 cm \times 9 cm\). When \(11\) spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use \(π = 3.14\)].
Ans: \(cm^3\)