**Ex 6.1,5**

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 When stone is dropped into a lake waves move in a circle at the speed of 5 cm/sec Thus, ๐๐๏ทฎ๐๐ก๏ทฏ = 5cm/sec We need find how fast area increasing w. r. t time when radius is 8cm i.e. we need to find ๐๐ด๏ทฎ๐๐ก๏ทฏ when r = 8 cm. We know that Area of circle = ฯr2 A = ฯr2 Different w. r. t time ๐๐ด๏ทฎ๐๐ก๏ทฏ = ๐(๐๐2)๏ทฎ๐๐ก๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = ฯ ๐(๐2)๏ทฎ๐๐ก๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = ฯ ๐(๐2)๏ทฎ๐๐ก๏ทฏ ร ๐๐๏ทฎ๐๐๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = ฯ ๐(๐2)๏ทฎ๐๐๏ทฏ ร ๐๐๏ทฎ๐๐ก๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = ฯ ร 2r. ๐๐๏ทฎ๐๐ก๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = 2ฯr . ๐ ๐๏ทฎ๐ ๐๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ = 2ฯr . 5 ๐๐ด๏ทฎ๐๐ก๏ทฏ = 10ฯr When r = 8 cm ๐๐ด๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ = 8๏ทฏ = 10 ร ฯ ร 8 ๐๐ด๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ = 8๏ทฏ = 80ฯ Since Area is in cm2 & time is in sec ๐๐ด๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ = 8๏ทฏ= 80ฯ ๐๐2๏ทฎ๐ ๐๐๏ทฏ ๐๐ด๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ = 8๏ทฏ= 80ฯ cm2/sec Hence Area is increasing at the rate of 80ฯ cm2/sec when r = 8 cm

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.