$\"\"$

The work done can be calculated by using the formula $\"\"$ .

$\"\"$ represents density, which is constant at $\"\"$ .

Where $\"\"$ and $\"\"$ .

Calculate $\"\"$ :

Find the general equation for the area of a slice of the tank at any given point.

$\"\"$

$\"\"$ is nothing but the height of the tank, since the tank is being filled the height is $\"\"$ .

Volume of the disk is $\"\"$ .

Weight of the disk is $\"\"$ .

Distance the disk of the water moved is $\"\"$ .

$\"\"$

The work done can be calculated by using the formula $\"\"$ .

Substiute the values in the formula.

$\"\"$

Apply integration :

$\"\"$

The work done to fill the tank with water through a hole in the base is

$\"\"$ or $\"\"$ .