Question

The cost of painting the total outside surface of a closed cylindrical oil tank at $60$ paise per sq. dm is $Rs237.60$. The height of the tank is $6$ times the radius of the base of the tank. Find its volume correct to two decimal places.

Answer 1

Let $r$ dm be the radius of the base and $h$ dm be the height of the cylindrical tank.

Then, $h=6r$ (given)

Total surfacea area $=2\pi r(r+h)=2\pi r(r+6r)=14\pi r^2$

cost of painting $=Rs.\left(14\pi r^2\right)\times \frac{60}{100}=Rs\frac{42}{5}{r}^2$

It is given that the cost of painting is Rs. $237.60$

$\therefore \frac{42}{5}\pi r^2=237.60\Rightarrow \frac{42}{5}\times \frac{22}{7}\times r^2=237.60$

$\Rightarrow r^2=237.60\times \frac{5}{42}\times \frac{7}{22}=9\Rightarrow r=3dm$

$\therefore h=6r=18dm$

Hence, volume of the cylinder $=\pi r^{2}h=(\pi \times 3\times 3\times 18){dm}^3=(\frac{22}{7}\times 9\times 18){dm}^3=509.14{dm}^3$