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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