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Ex 6.4, 7 - Find approx error in calculating surface area sphere

Ex 6.4,7 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Ex 6.4, 7 If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.Let r be the radius of the sphere Given r = 9 m Error in measurement of radius = ∆𝑟 ∆𝑟 = 0.03 m Surface area of the sphere = S = 4𝜋𝑟^2 We need to find the error in calculating the surface area ∆ S ∆ S = 𝑑𝑠/𝑑𝑟×∆"r" = (𝑑("4" 𝜋𝑟^2))/𝑑𝑟×∆"r" = "4" 𝜋 (𝑑(𝑟^2))/𝑑𝑟×∆"r" = 8𝜋r × 0.03 = 8𝜋(9) (0.03) = 2.16𝜋 hence the approximate error is 2.16𝝅 m2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.