Question

The capacity of a closed cylindrical vessel of height $1m$ is $15.4$ litres. How many square metres of metal sheet would be needed to make it?

Answer 1

Given data is as follows:

Volume of the cylinder $=15.4$ litres and height $h=1m$

We have to find the area of the sheet required to make this cylinder.

We know that $1000$ litre $=1m^3$
$\Rightarrow 1$ litre $=\frac{1}{1000}{m}^3$

Therefore, $15.4$ liters $=\frac{15.4}{1000}{m}^3$

We know that, Volume $=\pi r^{2}h$

Therefore, $\pi r^{2}h=\frac{15.4}{1000}$
$\Rightarrow \frac{22}{7}\times 1\times r^2=\frac{154}{10000}$
$\Rightarrow r^2=\frac{154}{10000}\times \frac{7}{22}$
$\Rightarrow r^2=\frac{7\times 7}{10000}$
$\Rightarrow r^2=(\frac{7}{100}{)}^2$
$\therefore r=\frac{7}{100}$

Now, using this radius we have to find the Total Surface Area.

Total Surface Area $=2\pi rh+2\pi r^2$
$=2\pi r(h+r)$

$=2\times \frac{22}{7}\times \frac{7}{100}(1+\frac{7}{100})$
$=\frac{44}{100}\left(\frac{100+7}{100}\right)$
$=\frac{44}{100}\times \frac{107}{100}$
$=0.4708m^2$
Therefore, $0.4708m^2$ of metal sheet required to make cylindrical vessel.