Question

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

Answer 1

Diameter of cylindrical tank = 4.2 m

$\therefore$ Radius (r) = $\frac{4.2}{2}$ = 2.1 m and height (h) = 4.5 m

(i) $\therefore$ Lateral surface area = $2\pi$ rh

=$2\times \frac{22}{7}\times 2.1\times 4.5m^2=59.4m^2$

(ii) Total surface area = $2\pi$ r (h + r)

=$2\times \frac{22}{7}\times 2.1(4.5+2.1)m^2$

= 13.2 $\times$ 6.6 = 87.12 $m^2$

Let total area of the sheet = $x{m}^2$

$\therefore$ Wastage = $\frac{1}{12}x{m}^2$

Remaining area of sheet = $x-\frac{1}{12}x=\frac{11}{12}x$

$\therefore \frac{11}{12}x=87.12\Rightarrow x=\frac{87.12\times 12}{11}$ = 95.04

$\therefore$ Total area of the sheet required = 95.04 $m^2$