Example 3 - A stone is dropped into a quiet lake, waves move - Finding rate of change

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 3 A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing? Let r be the radius of circle & A be the Area of circle When stone dropped into a lake wavers movie in circle at speed to 4 cm per sec. i.e. radius of circle increasing at a rate of 4 cm / sec. i.e. = 4 cm/sec. And we need to calculate how fast area increasing when waves is 10cm We need to calculate at r = 10 We know that Area of circle is r2 Now = ( 2) = ( 2) = 2 = 2 = 2 = 2 = [8r] Thus, = (8 r) When r = 10 =10 = 8(10) =10 =80 Since Area is in cm2 & time is in sec = 80 2 Hence the area is increasing at the rate of 80 cm2/sec,

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.