# 2. 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 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 that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

The volume of air present  =   Volume of cylinder   +   2 (Volume of a cone)

Now, the volume of a cylinder :    $=\ \pi r^2h$

or                                         $=\ \pi \left ( \frac{3}{2} \right )^2\times 8$

or                                         $=\ 18\pi \ cm^3$

And the volume of a cone is :

$=\ \frac{1}{3} \pi r^2h$

or                                          $=\ \frac{1}{3} \pi \times \left ( \frac{3}{2} \right )^2\times 2$

or                                          $=\ \frac{3}{2} \pi \ cm^3$

Thus the volume of air is :

$=\ 18 \pi\ +\ 2\times \frac{3}{2} \pi \ =\ 21\pi$

or                                      $=\ 66\ cm^3$

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