Question

Find:

$\left(i\right)$The lateral or curved surface area of a closed cylindrical petrol storage tank that is $4.2$ m in diameter and $4.5$ m high. [Assume $\pi =\frac{22}{7}$]
$\left(ii\right)$How much steel was actually used if $\frac{1}{12}$ of the steel actually used was wasted in making the tank?

Answer 1

(i) Height ($h$) of cylindrical tank $=4.5$. So, radius of the circular end $=\frac{4.2}{2}=2.1m$

The curved surface area of tank $=2\pi rh$

$=2\times \frac{22}{1}\times 2.1\times 4.5m^2=54.4m^2$

TSA of the tank $=2\pi r(r+h)$

$=2\times \frac{22}{1}\times 2.1(2.1+4.5)$

$=44\times 0.3\times 6.6$

$=87.12m^2$

(ii) Let amount of steel used in making the tank $=x$

Steel wasted $=\frac{x}{12}$.

Given:- Amount of steel required $-$ Amount of steel wasted $=$ TSA of the tank

$x-\frac{x}{12}=87.12$

$\frac{12x-x}{12}=87.12$

$\Rightarrow \frac{11x}{12}=\frac{8712}{100}$

$\Rightarrow x=95.04m^2$

$\therefore 95.04m^2$ steel was used in actual while making such a tank.