# 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 $6160\ m^3$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

92 Views