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 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.) [Use\( \pi=\frac{22}{ 7}\) ]

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 = \(\frac{3}{2}\) cm

Volume of air present in the model = Volume of cylinder + 2 × Volume of cones 
\(=\pi 𝑟^2ℎ_2+2×\frac{1}{ 3}\pi 𝑟^2ℎ_1\)

\(=\pi (\frac{3 }{2}) ^2 .8+2×\frac{1}{ 3}\pi (\frac{3}{ 2})^ 2 .2\)

\(=18\pi+3\pi=21\pi\)

\(=21×\frac{22}{ 7}\)
= 66 𝑐𝑚³