Arock is thrown into a still pond and causes a circular ripple. if the radius of the ripple is increasing at 2 ft/sec, how fast is the area changing when the radius is 5 ft? 10 ft?

Given:

Rate of increase in ripple radius, = 2 ft/sec

Solution:

Area of circle =

Differentiating w.r.t 'r', we get:

=  2

Rate of change in area is given by:

=  .

                                                                             (by chain rule)

= 2  .

when radius, r = 5ft

= 2  . 2 = 20

Now,

when r = 10 ft

= 2  .

= 2  . 2 = 40

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