A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is $ 20 \mathrm{~m} $. The heights of the cylindrical and conical portions are $ 4.2 \mathrm{~m} $ and $ 2.1 \mathrm{~m} $ respectively. Find the volume of the tent.
Given:
A circus tent has cylindrical shape surmounted by a conical roof.
The radius of the cylindrical base is \( 20 \mathrm{~m} \).
The heights of the cylindrical and conical portions are \( 4.2 \mathrm{~m} \) and \( 2.1 \mathrm{~m} \) respectively.
To do:
We have to find the volume of the tent.
Solution:
Radius of the tent $r = 20\ m$
Height of the conical part $h_1 = 2.1\ m$
Height of the cylindrical part $h_2 = 4.2\ m$
Total volume of the tent $=\frac{1}{3} \pi r^{2} h_{1}+\pi r^{2} h_{2}$
$=\pi r^{2}(\frac{1}{3} h_{1}+h_{2})$
$=\frac{22}{7}(20)^{2}(\frac{1}{3} \times 2.1+4.2)$
$=\frac{22 \times 400}{7}(0.7+4.2)$
$=\frac{22 \times 400}{7} \times 4.9$
$=6160 \mathrm{~m}^{3}$
The volume of the tent is $6160\ m^3$.
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