Last updated at May 6, 2021 by Teachoo

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Ex 6.1, 5 A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?Let r be the radius of circle & A be the Area of circle Given that When stone is dropped into a lake waves move in a circle at speed of 5 cm/sec i.e. Radius of circle increasing at a rate of 4 cm / sec. i.e. ๐ ๐/๐ ๐ = 5 cm/sec We need find how fast area increasing when radius is 8 cm i.e. we need to find ๐ ๐จ/๐ ๐ when r = 8 cm. We know that Area of circle = ฯr2 Now, ๐ ๐จ/๐ ๐ = (๐ (๐ ๐๐))/๐ ๐ ๐๐ด/๐๐ก = ฯ (๐(๐2))/๐๐ก ๐๐ด/๐๐ก = ฯ (๐(๐2))/๐๐ก ร ๐๐/๐๐ ๐๐ด/๐๐ก = ฯ (๐(๐2))/๐๐ ร ๐๐/๐๐ก ๐๐ด/๐๐ก = ฯ ร 2r ร ๐ ๐/๐ ๐ ๐๐ด/๐๐ก = 2ฯr ร 5 ๐๐ด/๐๐ก = 10ฯr When r = 8 cm โ ๐๐ด/๐๐กโค|_(๐ = 8) = 10 ร ฯ ร 8 โ ๐๐ด/๐๐กโค|_(๐ = 8) = 80ฯ Since Area is in cm2 & time is in sec โ ๐๐ด/๐๐กโค|_(๐ = 8)= 80ฯ cm2/sec Hence Area is increasing at the rate of 80ฯ cm2/sec when r = 8 cm

Ex 6.1

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Chapter 6 Class 12 Application of Derivatives

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.