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 aluminum 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.)

Answer 1

From the figure, it can be observed that

Height (h₁) of each conical part = 2 cm

Height (h₂) of cylindrical part = 12 − 2 × Height of conical part

= 12 − 2 ×2 = 8 cm

Radius (r) of cylindrical part = Radius of conical part =

Volume of air present in the model = Volume of cylinder + 2 × Volume of cones

$$\begin{gathered} =\mathrm{\pi }\times \frac{9}{4}\times 8+\frac{2}{3}\mathrm{\pi }\times \frac{9}{4}\times 2 \\ =18\mathrm{\pi }+3\mathrm{\pi } \\ =21\mathrm{\pi } \\ =66{\mathrm{cm}}^3 \end{gathered}$$