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A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds.

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meerkat18

The radius of the circle, in cm, after t seconds would be 50t 
The area, A, of the circle after t seconds is expressed in the equation: A = pi r^2 
A = pi (50T)^2 = pi2500t^2 
The change of area per unit time is obtained by differentiating the equation
A' = pi25002t A' = pi5000t
when t = 3 secondsA' = pi5000*3 = 47122 cm2/s

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