$\"\"$

Radius of the layer is $\"\"$ .

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

The water weighs $\"\"$ .

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

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

The weight of the layer is $\"\"$ .

$\"\"$

Calculate the work done in filling the tank half full of water through a hole in the bottom using \ \ water from the stream :

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Apply integration :

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The work done in filling the tank half full of water through a hole in the bottom using water from the stream is $\"\"$ .