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Example 1 - Find rate of change of area of circle per second

Example 1 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Example 1 Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm.We have to find rate of change of area of circle with respect to radius i.e. we need to find (𝒅(𝑨𝒓𝒆𝒂 𝒐𝒇 π’„π’Šπ’“π’„π’π’†))/(𝒅 (π’“π’‚π’…π’Šπ’–π’” 𝒐𝒇 π’„π’Šπ’“π’„π’π’†)) = 𝒅𝑨/𝒅𝒓 We know that Area of circle = Ο€ r2 A = Ο€r2 Finding 𝒅𝑨/𝒅𝒓 𝑑𝐴/π‘‘π‘Ÿ = (𝑑(πœ‹π‘Ÿ2))/π‘‘π‘Ÿ = Ο€ ((π‘Ÿ2))/π‘‘π‘Ÿ = Ο€ (2r) = 2Ο€r For r = 5 cm 𝑑𝐴/π‘‘π‘Ÿ = 2Ο€ (5) = 10Ο€ cmx/s

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Davneet Singh

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.