Rachel, an engineering student, was asked to make a model shaped … - Vidyadip

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).

✓

Answer

For upper conical portion
Radius of the base$(r) = 1.5\ cm$
Height $(h_1) = 2 cm$
$\therefore$ Volume $ =\frac13 \pi r^2h_1= \frac13 \pi (1.5)^2(2) = 1.5 \pi\ cm^3$

For lower conical portion
Volume $= 1.5 \pi\ cm^3$
For central cylindrical portion
Radius of the base $(r) = 1.5 cm$
Height $ (h_2) = 12 - (2 + 2) = 12 - 4 = 8 cm$
$\therefore$ Volume $= \pi r^2h_2= \frac13 \pi (1.5)^2(8)= 18 \pi\ cm^3$
Therefore, volume of the model $= 1.5 \pi + 1.5 \pi + 18 \pi = 21 \pi = 21 \times \frac{22}7 = 66\ cm^3$
Hence, the volume of the air contained in the model that Rechel made is $66\ cm^3$.

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