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The area of a circle is A=πR2 , as a function of time (in seconds) it is A(t)=π(Rt)2

Find the derivative of the area with respect to the radius

dA/dR=A'(t)=2πRt

So the rate the area is increasing at 7s is given by

A'(7)=2π(70X7)=980π cm/s2 or 3078.76 cm/s2

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