A cylindrical vessel contains 154 litres of water. If the radius of the base is 14 cm, the height (in cm) of the water column in the vessel is:

The correct option is 250 cm.

Step 1: Understand the given dimensions

We are given:

Volume of water in the cylindrical vessel, $V=154\text{litres}$

Radius of the base of the cylinder, $r=14\text{cm}$

Step 2: Convert the volume from litres to cubic centimetres (cm³)

Since 1 litre equals 1000 cm³:

$V=154\times 1000=154000{\text{cm}}^3$

Step 3: Apply the formula for the volume of a cylinder

The volume $V$ of a cylindrical column of height $h$ is given by the formula:

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

Step 4: Substitute the given values and solve for height ($h$)

Using $\pi =\frac{22}{7}$:

$154000=\frac{22}{7}\times {14}^2\times h$

Simplify the right-hand side:

$154000=\frac{22}{7}\times 14\times 14\times h$

$154000=22\times 2\times 14\times h$

$154000=616\times h$

Now, divide both sides by 616 to find $h$:

$h=\frac{154000}{616}$

$h=250\text{cm}$

Thus, the height of the water column in the vessel is 250 cm.