Question

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

Answer 1

$\left(i\right)$Diameter of a cylindrical(closed) petrol tank$=4.2m$

Radius$=\frac{4.2}{2}=2.1m$

Height$=4.5m$

Curved Surface area$=2\pi rh=2\times \frac{22}{7}\times 2.1\times 4.5=59.4sq.m$

$\left(ii\right)$Total surface area$=2\pi r(r+h)=2\times \frac{22}{7}\times 2.1\times (2.1+4.5)=2\times \frac{22}{7}\times 2.1\times 6.6=87.12sq.m$

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

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

Given:Amount of steel required$-$Amount of steel wasted$=$T.S.A of the tank.

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

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

$\Rightarrow \frac{11x}{12}=87.12$

$\Rightarrow x=\frac{12}{11}\times 87.12=95.04sq.m$

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