I need help solving this problem

Question

. A pebble is dropped in a pond, and circular ripples spread out from the point of impact. The radius of
the circle from the outermost ripple is increasing at a constant rate of 4 inches per second. What is the
rate of change of the area of the circle formed by this ripple at the moment the radius is 5 inches?

Answer 1

Area = pi·r²

 

d(Area)/dt = pi·(dr²/dr)·(dr/dt)

 

d(Area)/dt = pi·2r·(dr/dt)

 

Now dr/dt = 4 in/sec and r = 5 in.  Plug those values in and compute d(Area)/dt.

Answer 2

Here dr/dt = 4 inches per second and when r = 5 inches, dA/dt =?

A = πr²

dA/dt = 2πr. dr/dt

           = 2π(5).4

           = 40π inch²/second