Question

A cylinderical tank has a capacity of $6160cum.$ Find its depth if its radius is $14m.$ Calculate the cost of painting its curved outer surface at the rate of $Rs.3$ per square metre. $(Take\pi =\frac{22}{7})$

Answer 1

Let the depth of the tank be $h$.

Given:-

Volume of tank $=6160m^3$

Radius of tank $=14m$

As we know that, volume of tank is given as-

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

Therefore,

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

$\Rightarrow \frac{22}{7}\times {\left(14\right)}^{2}h=6160$

$\Rightarrow 616h=6160$

$\Rightarrow h=\frac{6160}{616}=10m$

Hence the depth of the tank is $10m$

Now again as we know that the curved surface area of cylinder is given as-

$A=2\pi rh$

Therefore,

curved surface area of tank $=2\times \frac{22}{7}\times 14\times 10=880m^2$

Given that the cost of painting is $Rs.3\text{per}{m}^2$.

Therefore,

Cost of painting the curved outer surface of tank $=3\times 880=Rs.2640$

Hence the cost of painting the curved outer surface is $Rs.2640$.