A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is $\displaystyle 3$ cm and its total length is $\displaystyle 12$ cm. If each cone has a height of $\displaystyle 2$ cm, find the volume of air contained in the model.

Radius of each cone = Radius of cylinder \(\displaystyle =\frac{3}{2} \mathrm{~cm}\) Height of each cone 'H' = $\displaystyle 2$ cm Height of cylinder ' h ' \(\displaystyle =12-4=8 \mathrm{~cm}\) Volume of air = Volume of cylinder + Volume of $\displaystyle 2$ cones \[\begin{aligned} & =\pi r^{2} h+2 \frac{1}{3} \pi r^{2} H \\ & =\pi r^{2}\left(h+\frac{2}{3} H\right)=\frac{22}{7} \times \frac{3}{2} \times \frac{3}{2}\left(8+\frac{2}{3} \times 2\right) \\ & =\frac{22}{7} \times \frac{9}{4} \times \frac{28}{3}=66 \mathrm{~cm}^{3} \end{aligned} \]