web analytics

Ex 6.1, 6 - Radius of a circle is increasing at rate of 0.7 cm/s - Finding rate of change

Slide18.JPG

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
Ask Download

Transcript

Ex 6.1,6 The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference? Let r be the radius of circle & C be the circumference of circle Given that Radius of a circle is increasing at the rate of 0.7 cm/sec i.e. ๐‘‘๐‘Ÿ๏ทฎ๐‘‘๐‘ก๏ทฏ = 0.7 cm/sec We need find rate of change of circumference of circle w. r. ๐‘ก time i.e. we need to calculate ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ we know that Circumference of circle = 2ฯ€r i.e. C = 2ฯ€r Different w. r. t time ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = ๐‘‘(2๐œ‹๐‘Ÿ)๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 2ฯ€ ๐‘‘๐‘Ÿ๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 2ฯ€ ร— 0.7 ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4 ฯ€ Since circumference is in cm & time is in sec ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4ฯ€ ๐‘๐‘š๏ทฎ๐‘ ๐‘’๐‘๏ทฏ ๐‘‘๐‘๏ทฎ๐‘‘๐‘ก๏ทฏ = 1.4ฯ€ cm/sec Hence, circumference of circle is increasing at the rate of 1.4ฯ€cm/sec

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.
Jail