Ex 6.1, 3 - Radius of a circle is increasing uniformly at 3 cm/s

Ex 6.1,3 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,3 - Chapter 6 Class 12 Application of Derivatives - Part 3 Ex 6.1,3 - Chapter 6 Class 12 Application of Derivatives - Part 4

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

Transcript

Ex 6.1, 3 The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.Let r be the radius of circle . & A be the Area of circle. Given that Radius of a circle is increasing at the rate of 3 cm/s Thus, ๐’…๐’“/๐’…๐’• = 3 cm /sec We need to find rate of change of area of circle w. r. t time when r = 10 cm i.e. we need to find ๐’…๐‘จ/๐’…๐’• when r = 10 cm We know that Area of circle = ฯ€r2 A = ฯ€r2 Differentiating w.r.t time ๐’…๐‘จ/๐’…๐’• = ๐’…(๐…๐’“๐Ÿ)/๐’…๐’• ๐‘‘๐ด/๐‘‘๐‘ก = ฯ€ ๐‘‘(๐‘Ÿ2)/๐‘‘๐‘ก ๐‘‘๐ด/๐‘‘๐‘ก = ฯ€ ๐‘‘(๐‘Ÿ2)/๐‘‘๐‘ก ร— ๐’…๐’“/๐’…๐’“ ๐‘‘๐ด/๐‘‘๐‘ก = ฯ€ ๐’…(๐’“๐Ÿ)/๐’…๐’“ ร— ๐‘‘๐‘Ÿ/๐‘‘๐‘ก ๐‘‘๐ด/๐‘‘๐‘ก = ฯ€. 2r . ๐‘‘๐‘Ÿ/๐‘‘๐‘ก ๐‘‘๐ด/๐‘‘๐‘ก = 2ฯ€r . ๐’…๐’“/๐’…๐’• ๐‘‘๐ด/๐‘‘๐‘ก = 2ฯ€r . 3 ๐‘‘๐ด/๐‘‘๐‘ก = 6ฯ€r When ๐’“ = 10 cm โ”œ ๐‘‘๐ด/๐‘‘๐‘กโ”ค|_(๐‘Ÿ =10) = 6 ร— ฯ€ ร— 10 โ”œ ๐‘‘๐ด/๐‘‘๐‘กโ”ค|_(๐‘Ÿ =10) = 60 ฯ€ (From (1): ๐‘‘๐‘Ÿ/๐‘‘๐‘ก = 3) Since area is in cm2 & time is in sec ๐‘‘๐ด/๐‘‘๐‘ก = 60ฯ€ cm2/sec Hence, Area is increasing at the rate of 60ฯ€ cm2/sec when r = 10 cm

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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.