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Home » A stone is dropped into a quite lake and waves move in circles at the rate of 5 cm/sec. At the instant when radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
A stone is dropped into a quite lake and waves move in circles at the rate of 5 cm/sec. At the instant when radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
Applications of Derivatives | CBSE | Class 12 | Exercise 6.1 | Maths | NCERT
A stone is dropped into a quite lake and waves move in circles at the rate of 5 cm/sec. At the instant when radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

 Let  cm be the radius of the circular wave at time 

Rate of increase of radius of circular wave = 5 cm/sec

 is positive and = 5 cm/sec

Let  be the enclosed area of the circular wave.

 

Rate of change of area =  = 

=  = 

Putting  = 8 cm (given),

 =  cm2/sec

Since  is positive, therefore area of circular wave is increasing at the rate of  cm2/sec.

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