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Finding rate of change

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


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 = 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.