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

Ex 6.1,6 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,6 - Chapter 6 Class 12 Application of Derivatives - Part 3

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

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’“/๐’…๐’• = 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‘ช/๐’…๐’• We know that Circumference of circle = 2ฯ€r Now, ๐‘‘๐ถ/๐‘‘๐‘ก = (๐‘‘(2๐œ‹๐‘Ÿ))/๐‘‘๐‘ก ๐‘‘๐ถ/๐‘‘๐‘ก = 2ฯ€ ๐’…๐’“/๐’…๐’• ๐‘‘๐ถ/๐‘‘๐‘ก = 2ฯ€ ร— 0.7 ๐‘‘๐ถ/๐‘‘๐‘ก = 1.4ฯ€ (From (1): ๐‘‘๐‘Ÿ/๐‘‘๐‘ก = 5 ) Since circumference is in cm & time is in sec ๐‘‘๐ถ/๐‘‘๐‘ก = 1.4ฯ€ cm/sec Hence, circumference of circle is increasing at the rate of 1.4ฯ€ cm/sec

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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.