Answer:
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1) 72\(\pi\) cm² / min. ;
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2) 192 \(\pi\) cm² / min.
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Explanation:
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Area of a circle: A = \(\pi\) r² ;
Rate of change of Area is: da/dt = 2\(\pi\) r (dr/dt) ;
Given: dr/dt = 3 cm / min.
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Problem 1)
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dA/dt = 2 \(\pi\) (12 cm)(3 cm/ min) = 72 \(\pi\) cm² / min. ;
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Problem 2)
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dA/dt = 2 \(\pi\) (32 cm)(3 cm/ min) = 192 \(\pi\) cm² / min.
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