Question

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.

Answer 1

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 = pi*2500*t^2 
The change of area per unit time is obtained by differentiating the equation
A' = pi*2500*2*t A' = pi*5000*t
when t = 3 secondsA' = pi*5000*3 = 47122 cm2/s