Question

The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs. 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.

Answer 1

Rate of painting = 50 paise per $d{m}^2$

Total cost = Rs. 198

$\therefore$ Total surface area = $\frac{198\times 100}{50}d{m}^2$ = 396 $d{m}^2$

Let radius of the base (r) = x

Then height (h) = 6x

Now $2\pi$ r (r + h) = 396

$\Rightarrow 2\times \frac{22}{7}\times$ x(x+6x) = 396

$\Rightarrow \frac{44x}{7}$(7x)= 396

$\Rightarrow 44x^2=396\Rightarrow x^2=\frac{396}{44}$=9 $\Rightarrow x^2=9=(3{)}^2$

$\therefore$ x = 3 dm

$\therefore$ Radius = 3 dm

and height = 3 $\times$ 6 = 18 dm

Now volume = $\pi r^2$ h

=$\frac{22}{7}\times 3\times 3\times 18d{m}^3$

=$\frac{3564}{7}=509.14d{m}^3$