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  • 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 th

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.)

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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

                                           

Posted by

Devendra Khairwa

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