$\"\"$

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Diameter of the hemisphere is $\"\"$ cm.

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Radius of the basin is $\"\"$ cm.

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$\"\"$

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Basin is being filled with water at a rate of $\"\"$ L/min.

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$\"\"$ .

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$\"\"$ .

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Volume of the water at height $\"\"$ is given by $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Substitute $\"\"$ in above expression.

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$\"\"$ .

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

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$\"\"$

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When the hemispherical basin is half full, then $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in (1).

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$\"\"$

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Rate at which the water is rising in the basin when it is half full is $\"\"$ cm/min.

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$\"\"$

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Rate at which the water is rising in the basin when it is half full is $\"\"$ cm/min.