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.

 Given:

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.

To do:

We have to find the volume corrected to 2 decimal places.

Solution:

Rate of painting $= 50$ paise per $dm^2$

Total cost $= Rs.\ 198$

Total surface area $=\frac{198 \times 100}{50} \mathrm{dm}^{3}$

$=396 \mathrm{dm}^{2}$

Let the radius of the base be $x$

This implies,

Height $(h)=6 x$

Therefore,

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

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

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

$44 x^{2}=396$

$x^{2}=\frac{396}{44}$

$x^2=9$

$x^{2}=(3)^{2}$

$\Rightarrow x=3 \mathrm{dm}$

Radius $=3 \mathrm{dm}$

Height $=3 \times 6$

$=18 \mathrm{dm}$

Volume $=\pi r^{2} h$

$=\frac{22}{7} \times 3 \times 3 \times 18$

$=\frac{3564}{7}$

$=509.14 \mathrm{dm}^{3}$

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Updated on: 10-Oct-2022

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