SOLUTION: A stone is thrown into a lake and a circular ripple moves out at a constant speed of 1m/s. Find the rate of change of the circle’s area at the moment when t= 4s.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A stone is thrown into a lake and a circular ripple moves out at a constant speed of 1m/s. Find the rate of change of the circle’s area at the moment when t= 4s.      Log On


   

Question 1106185: A stone is thrown into a lake and a circular ripple moves out at a constant speed of 1m/s. Find the rate of change of the circle’s area at the moment when t= 4s.
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
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You are given for the radius R(t) = t, where "t" is time in seconds.


The area of the circle is A(t) = pi%2A%28R%28t%29%29%5E2 = pi%2At%5E2.


The rate of change of the circle’s area is  %28dA%29%2F%28dt%29 = 2%2Api%2At.


At t = 4 seconds,  %28dA%29%2F%28dt%29 = 2%2Api%2A4 = 2%2A3.14%2A4 = 25.12 m^2/s.

Solved.