Question

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 $3cm$ and its length is $12cm$. If each cone has a height of $2cm$, 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.)

Answer 1

For the given statement first draw a diagram,

In this diagram, we can observe that

Height ($h_1$) of each conical part $=2$ cm

Height ($h_2$) of cylindrical part $12-2-2=8$ cm

Radius ($r$) of cylindrical part = Radius of conical part = $\frac{3}{2}$ cm

Volume of air present in the model = Volume of cylinder $+$ $2\times$ Volume of a cone

$=\pi r^2{h}_2+2\times \frac{1}{3}\pi r^2{h}_1$

$=\pi {\left(\frac{3}{2}\right)}^2\times 8+2\times \frac{1}{3}\pi {\left(\frac{3}{2}\right)}^2\left(2\right)$

$=\pi \times \frac{9}{4}\times 8+\frac{2}{3}\pi \times \frac{9}{4}\times 2$

$=18\pi +3\pi =21\pi$

$=21\times \frac{22}{7}=66$ cm${}^2$