Rachel an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends by using thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm,find the volume of air contained in the model the Rachel made. (Assume the outer and inner dimensions of the model be nearly the same).

Volume of the air contained in the model = Volume of the cylindrical portion of the model + Volume of its two conical ends.

\( = \ \pi r^2 h_1 \ + \ 2 \ × \ \frac{1}{3} \pi r^2 h_2 \ \)
\( = \ \pi r^2(h_1 \ + \ \frac{2}{3} h_2) \)

where \( r \ = \ \frac{3}{2} \) cm , \(h_1 \ = \ 8 \) cm and \(h_2 \ = \ 2 \) cm

\( = \ \frac{22}{7} \ × \ ( \frac{3}{2})^2 \ × \ (8 \ + \ \frac{2}{3} \ × \ 2) \) \( = \ \frac{22}{7} \ × \ \frac{9}{4} \ × \ \frac{24 \ + \ 4}{3} \)

\(= \ \frac{22}{7} \ × \ \frac{9}{4} \ × \ \frac{28}{3} \) \( = \ 66 \) cm³