Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

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

Transcript

Ex 6.1, 1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cmLet Radius of circle = ๐‘Ÿ & Area of circle = A We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐’…๐‘จ/๐’…๐’“ We know that Area of Circle = A = ใ€–๐œ‹๐‘Ÿใ€—^2 Finding ๐’…๐‘จ/๐’…๐’“ ๐‘‘๐ด/๐‘‘๐‘Ÿ = (๐‘‘ (ใ€–๐œ‹๐‘Ÿใ€—^2 ))/๐‘‘๐‘Ÿ ๐‘‘๐ด/๐‘‘๐‘Ÿ = ๐œ‹ (๐‘‘ใ€–(๐‘Ÿใ€—^2))/๐‘‘๐‘Ÿ ๐‘‘๐ด/๐‘‘๐‘Ÿ = ๐œ‹(2๐‘Ÿ) ๐’…๐‘จ/๐’…๐’“ = ๐Ÿ๐…๐’“ When r = 3 cm ๐‘‘๐ด/๐‘‘๐‘Ÿ = 2ฯ€r Putting r = 3 cm โ”œ ๐‘‘๐ด/๐‘‘๐‘Ÿโ”ค|_(๐‘Ÿ = 3)= 2ฯ€ ร— 3 โ”œ ๐‘‘๐ด/๐‘‘๐‘Ÿโ”ค|_(๐‘Ÿ = 3) = 6ฯ€ Since Area is in cm2 & radius is in cm ๐‘‘๐ด/๐‘‘๐‘Ÿ = 6ฯ€ cm2/cm Hence, Area is increasing at the rate of 6ฯ€ cm2/ cm when r = 3 cm (ii) When r = 4 cm ๐‘‘๐ด/๐‘‘๐‘Ÿ = 2ฯ€r Putting r = 4 cm ๐‘‘๐ด/๐‘‘๐‘Ÿ = 2ฯ€ ร— 4 ๐‘‘๐ด/๐‘‘๐‘Ÿ = 8ฯ€ Since Area is in cm2 & radius is in cm ๐’…๐‘จ/๐’…๐’“ = 8ฯ€ cm2/cm Hence, Area is increasing at the rate of 8ฯ€ cm2/cm when r = 4 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 9 years. He provides courses for Maths and Science at Teachoo.