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

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

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 = โˆ†๐‘Ÿ โˆ†๐‘Ÿ = 0.03 m Surface area of the sphere = S = 4๐œ‹๐‘Ÿ^2 We need to find the error in calculating the surface area โˆ† S โˆ† S = ๐‘‘๐‘ /๐‘‘๐‘Ÿร—โˆ†"r" = (๐‘‘("4" ๐œ‹๐‘Ÿ^2))/๐‘‘๐‘Ÿร—โˆ†"r" = "4" ๐œ‹ (๐‘‘(๐‘Ÿ^2))/๐‘‘๐‘Ÿร—โˆ†"r" = 8๐œ‹r ร— 0.03 = 8๐œ‹(9) (0.03) = 2.16๐œ‹ hence the approximate error is 2.16๐… m2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.