$\"\"$

\

Observe the figure:

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The Depth is $\"\"$ .

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The length is $\"\"$ .

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Redraw the figure:

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$\"\"$

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The semicircle is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

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Length of the semicircle is $\"\"$ .

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The weight density of water is $\"\"$ .

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The limits range from $\"\"$ to $\"\"$ .

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$\"\"$

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The fluid force is: $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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If $\"\"$ then $\"\"$ .

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if $\"\"$ then $\"\"$ .

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$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, the fluid force is $\"\"$ .

\

$\"\"$

\

The fluid force is $\"\"$ .