Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 6 \(cm\) and its length is 38 \( cm\). If each cone has a height of \(2 cm\), find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.) [Note: Take \(\pi = \frac{22}{7}\)]
Volume of air contained in the model \(=\) _____________ \(cm^3\)