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Question
Find the rate of change of the area of a circle with respect to its radius r when r = 4 cm.
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Solution
The area of a circle (A) with radius (r) is given by,
`A = pir^2`
Now, the rate of change of the area with respect to its radius is given by,
`(dA)/(dr) = (d)/(dr)(pir^2) = 2pir`
When r = 4 cm,
`(dA)/(dr) = 2pi (4) = 8pi`
Hence, the area of the circle is changing at the rate of 8π cm when its radius is 4 cm.
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