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Ex 6.1, 1 Class 12 Maths - Find rate of change of area of a circle

Ex 6.1, 1 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1, 1 - Chapter 6 Class 12 Application of Derivatives - Part 3 Ex 6.1, 1 - Chapter 6 Class 12 Application of Derivatives - Part 4

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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 = π‘Ÿ & Area of circle = A We need to find rate of change of Area w. r. t Radius i.e. we need to calculate 𝒅𝑨/𝒅𝒓 We know that Area of Circle = A = γ€–πœ‹π‘Ÿγ€—^2 Finding 𝒅𝑨/𝒅𝒓 𝑑𝐴/π‘‘π‘Ÿ = (𝑑 (γ€–πœ‹π‘Ÿγ€—^2 ))/π‘‘π‘Ÿ 𝑑𝐴/π‘‘π‘Ÿ = πœ‹ (𝑑〖(π‘Ÿγ€—^2))/π‘‘π‘Ÿ 𝑑𝐴/π‘‘π‘Ÿ = πœ‹(2π‘Ÿ) 𝒅𝑨/𝒅𝒓 = πŸπ…π’“ When r = 3 cm 𝑑𝐴/π‘‘π‘Ÿ = 2Ο€r Putting r = 3 cm β”œ 𝑑𝐴/π‘‘π‘Ÿβ”€|_(π‘Ÿ = 3)= 2Ο€ Γ— 3 β”œ 𝑑𝐴/π‘‘π‘Ÿβ”€|_(π‘Ÿ = 3) = 6Ο€ Since Area is in cm2 & radius is in cm 𝑑𝐴/π‘‘π‘Ÿ = 6Ο€ cm2/cm Hence, Area is increasing at the rate of 6Ο€ cm2/ cm when r = 3 cm (ii) When r = 4 cm 𝑑𝐴/π‘‘π‘Ÿ = 2Ο€r Putting r = 4 cm 𝑑𝐴/π‘‘π‘Ÿ = 2Ο€ Γ— 4 𝑑𝐴/π‘‘π‘Ÿ = 8Ο€ Since Area is in cm2 & radius is in cm 𝒅𝑨/𝒅𝒓 = 8Ο€ cm2/cm Hence, Area is increasing at the rate of 8Ο€ cm2/cm when r = 4 cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.