$\"\"$

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

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

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

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Calculate $\"\"$ :

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

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$\"\"$

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

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

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

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

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$\"\"$

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

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Substiute the values in the formula.

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$\"\"$

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Apply integration :

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$\"\"$

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$\"\"$

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

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