Rate of Change of Area of circle with respect to radius r at r = 6 cm

Ex 6.1,17 - Chapter 6 Class 12 Application of Derivatives - Part 2


Ex 6.1, 17 The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10πœ‹ (B) 12πœ‹ (C) 8πœ‹ (D) 11πœ‹Let r be the radius of circle & A be the area of circle We need to find Rate of change of Area of circle w.r.t to radius at π‘Ÿ = 6 i.e. we need to find 𝒅𝑨/𝒅𝒓 at 𝒓 = 6 We know that Area of circle = A = πœ‹ π‘Ÿ^2 Differentiating w.r.t π‘Ÿ 𝑑𝐴/π‘‘π‘Ÿ=𝑑(πœ‹π‘Ÿ^2 )/π‘‘π‘Ÿ 𝑑𝐴/π‘‘π‘Ÿ=πœ‹ 𝑑(π‘Ÿ^2 )/π‘‘π‘Ÿ 𝑑𝐴/π‘‘π‘Ÿ=πœ‹ . 2r 𝒅𝑨/𝒅𝒓=πŸπ…π’“ Putting π‘Ÿ = 6 〖𝑑𝐴/π‘‘π‘Ÿβ”‚γ€—_(π‘Ÿ = 6" " )=2πœ‹(6) 〖𝑑𝐴/π‘‘π‘Ÿβ”‚γ€—_(π‘Ÿ = 6" " )=πŸπŸπ… Hence, Correct answer is B

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.