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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

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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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