$\"\"$

The cylindrical tank radius is $\"\"$ m.

Tank is being filled with water at a rate of $\"\"$ m³/min.

Therefore rate of increase of volume $\"\"$ .

The volume of the cylinder is $\"\"$ .

where $\"\"$ is height of the cylinder.

$\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$ in above expression.

$\"\"$

Height of the water increases at rate of $\"\"$ m/min.

The height of water is increasing at a rate of $\"\"$ m/min.