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Ex 6.1, 3 - Radius of a circle is increasing uniformly at 3 cm/s

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

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Ex 6.1, 3 The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.Let r be the radius of circle . & A be the Area of circle. Given that Radius of a circle is increasing at the rate of 3 cm/s Thus, 𝒅𝒓/𝒅𝒕 = 3 cm /sec We need to find rate of change of area of circle w. r. t time when r = 10 cm i.e. we need to find 𝒅𝑨/𝒅𝒕 when r = 10 cm We know that Area of circle = Ο€r2 A = Ο€r2 Differentiating w.r.t time 𝒅𝑨/𝒅𝒕 = 𝒅(π…π’“πŸ)/𝒅𝒕 𝑑𝐴/𝑑𝑑 = Ο€ 𝑑(π‘Ÿ2)/𝑑𝑑 𝑑𝐴/𝑑𝑑 = Ο€ 𝑑(π‘Ÿ2)/𝑑𝑑 Γ— 𝒅𝒓/𝒅𝒓 𝑑𝐴/𝑑𝑑 = Ο€ 𝒅(π’“πŸ)/𝒅𝒓 Γ— π‘‘π‘Ÿ/𝑑𝑑 𝑑𝐴/𝑑𝑑 = Ο€. 2r . π‘‘π‘Ÿ/𝑑𝑑 𝑑𝐴/𝑑𝑑 = 2Ο€r . 𝒅𝒓/𝒅𝒕 𝑑𝐴/𝑑𝑑 = 2Ο€r . 3 𝑑𝐴/𝑑𝑑 = 6Ο€r When 𝒓 = 10 cm β”œ 𝑑𝐴/𝑑𝑑─|_(π‘Ÿ =10) = 6 Γ— Ο€ Γ— 10 β”œ 𝑑𝐴/𝑑𝑑─|_(π‘Ÿ =10) = 60 Ο€ (From (1): π‘‘π‘Ÿ/𝑑𝑑 = 3) Since area is in cm2 & time is in sec 𝑑𝐴/𝑑𝑑 = 60Ο€ cm2/sec Hence, Area is increasing at the rate of 60Ο€ cm2/sec when r = 10 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.