Question

The capacity of a closed cylindrical vessel of height $1m$ is$15.4liters$. How many square meters of metal sheet would be needed to make it? (Assume $\pi =\frac{22}{7}$)

Answer 1

Step 1: Find the radius of the cylinder :

Given

Height of cylinder$\left(h\right)=1m=100cm$

Volume of cylinder $\left(V\right)=15.4liters$

We know that $1liter=1000c{m}^3$

So, $15.4liters=15.4\times 1000c{m}^3$

$V=15,400c{m}^3$

We know that

Volume of cylinder $=\pi r^{2}h$

$$\begin{gathered} \Rightarrow 15,400=\frac{22}{7}\times r^2\times 100 \\ \Rightarrow r^2=\frac{15400X7}{22\times 100} \\ \Rightarrow r^2=49 \\ \Rightarrow r=\surd 49 \\ \Rightarrow r=7cm \end{gathered}$$

Thus, the radius is $7cm$

Step 2: Find the total surface area :

We know that,

The total surface area of cylinder$=2\mathrm{\pi r}\left(\mathrm{r}+\mathrm{h}\right)$

$\begin{array}{rcl}& =& 2\times \frac{22}{7}\times 7\times (7+100)\\ & =& 2\times 22\times 107\\ & =& 4708c{m}^2\\ & =& 0.4708m^2(\sin ce1cm=\frac{1}{100}m)\end{array}$

Hence, $0.4708m^2$ of a metal sheet would be needed to make it.