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Ex 6.1, 6 - Radius of a circle is increasing at rate of 0.7 cm/s

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

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Ex 6.1, 6 The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference? Let r be the radius of circle & C be the circumference of circle Given that Radius of a circle is increasing at the rate of 0.7 cm/sec i.e. 𝒅𝒓/𝒅𝒕 = 0.7 cm/sec We need find rate of change of circumference of circle w. r. 𝑑 time i.e. we need to calculate 𝒅π‘ͺ/𝒅𝒕 We know that Circumference of circle = 2Ο€r Now, 𝑑𝐢/𝑑𝑑 = (𝑑(2πœ‹π‘Ÿ))/𝑑𝑑 𝑑𝐢/𝑑𝑑 = 2Ο€ 𝒅𝒓/𝒅𝒕 𝑑𝐢/𝑑𝑑 = 2Ο€ Γ— 0.7 𝑑𝐢/𝑑𝑑 = 1.4Ο€ (From (1): π‘‘π‘Ÿ/𝑑𝑑 = 5 ) Since circumference is in cm & time is in sec 𝑑𝐢/𝑑𝑑 = 1.4Ο€ cm/sec Hence, circumference of circle is increasing at the rate of 1.4Ο€ cm/sec

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