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Metal spheres, each of radius \(2 cm\), are packed into a rectangular box of internal dimensions \(16 cm \times 8 cm \times 8 cm\). When \(16\) 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: \(cm^3\)