Solve the following related rates problems:

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ??/?. How rapidly is the area enclosed by the ripple increasing at the end of 10 ??

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Step 1A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ??/?. How rapidly is the area enclosed by the ripple increasing at the end of 10 ?? Step 2We have rate of constant drdt=3  and radius=10We know that,       Area of circle(A)=πr2           ........(1)Differentiation equation (1) w.r.t time (t), we have         ⇒dAdt=ddtπr2  ⇒dAdt=2πrdrdtAt drdt=3 and r=10  ⇒dAdt=2π×10×3  ⇒dAdt=60π sq. unitsHence, dAdt=60π sq. units ...