Question

The capacity of a closed cylindrical vessel of height $1m$ is $15.4L$.

How many square metres of metal sheet would be needed to make it?

Answer 1

Height of cylindrical vessel $=1m$
Capacity of the cylindrical vessel $=15.4L$
$=\frac{15.4}{1000}=.0154m^3$ [$\because 1L=\frac{1}{1000}{m}^3$]

Volume of a cylinder $=\pi r^{2}h$
$\Rightarrow \frac{22}{7}\times r^2\times 1=0.0154$
$\Rightarrow r^2=\frac{7}{22}\times 0.0154$

$\Rightarrow r^2=7\times 0.0007$

$\Rightarrow r^2=0.0049$

$\Rightarrow r^2=\frac{49}{10000}$

$\Rightarrow r=\sqrt{\frac{49}{10000}}$

$\Rightarrow r=\frac{7}{100}$

$\Rightarrow r=0.07m$
Therefore, Required metal of sheet $=$ TSA of cylindrical vessel

$=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 0.07m\times (0.07+1)m$

$=44\times 0.01\times 1.07$

$=0.4708m^2$

Therefore, $0.4708m^2$ of sheet will be required to make the vessel.