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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.