Question

A cylindrical tank of diameter $35$ cm is full of water. If $11$ litres of water is drawn out, the water level in the tank will drop by _________.

• A. $10\frac{1}{2}$ cm
• B. $11\frac{3}{7}$ cm
• C. $12\frac{6}{7}$ cm
• D. $14$ cm

Answer 1

The correct option is B $11\frac{3}{7}$ cm

Given,diameter of the tank is $35$ cm.

Therefore, radius of the tank, $r=\frac{35}{2}$ cm

Volume of a cylinder $=$ $\pi r^{2}h$,

where, $r$ is the radius of the cylinder

and $h$ is the height of the cylinder.

Height of the water level will be decreased corresponding the volume of water removed.

Which means, the height of the water level occupying $11$ litres of volume is the height decreased when it is removed.

$\Rightarrow$ $V=11$ litres

$\Rightarrow r=\frac{35}{2}$ cm

From the formula, $V=\pi r^{2}h$

$11\times {10}^3=\frac{22}{7}\times {\left(\frac{35}{2}\right)}^2\times h$ ($\because \pi =\frac{22}{7}$ and $1$ Lire $=1000{\text{cm}}^3$)

On simplifying, we get

$h=\frac{80}{7}=11\frac{3}{7}$ cm

Therefore, option B is correct