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

Transcript

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) 10p (B) 12p (C) 8p (D) 11p 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 𝑟 = 6 i.e. we need to find 𝑑𝐴﷮𝑑𝑟﷯ at 𝑟 = 6 We know that Area of circle = 𝜋 𝑟﷮2﷯ i.e. A = 𝜋 𝑟﷮2﷯ Diff w.r.t 𝑟 𝑑𝐴﷮𝑑𝑟﷯= 𝑑 𝜋 𝑟﷮2﷯﷯﷮𝑑𝑟﷯ 𝑑𝐴﷮𝑑𝑟﷯=𝜋 𝑑 𝑟﷮2﷯﷯﷮𝑑𝑟﷯ 𝑑𝐴﷮𝑑𝑟﷯=𝜋 . 2r 𝑑𝐴﷮𝑑𝑟﷯=2𝜋𝑟 We need to 𝑑𝐴﷮𝑑𝑟﷯ when 𝑟 = 6 𝑑𝐴﷮𝑑𝑟﷯│﷮𝑟 = 6 ﷯=2𝜋 6﷯ 𝑑𝐴﷮𝑑𝑟﷯│﷮𝑟 = 6 ﷯=12𝜋 Hence correct answer is B