Ex 6.4, 6 - If radius of a sphere is measured 7 m , error 0.02 m

Ex 6.4,6 - 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, 6 If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.Let r be the radius of the sphere Given r = 7 m Error in measurement of radius = โˆ†r โˆ†r = 0.02 m Volume of the sphere = V = 4/3 ๐œ‹๐‘Ÿ^3 We need to find error in calculating the volume that is โˆ†v โˆ†V = ๐‘‘๐‘ฃ/๐‘‘๐‘Ÿ ร— โˆ†r = ๐‘‘(4/3 ๐œ‹๐‘Ÿ^3 )/๐‘‘๐‘Ÿ ร— โˆ†r = 4/3 ๐œ‹ (๐‘‘(๐‘Ÿ^3))/๐‘‘๐‘Ÿร—โˆ†r = 4/3 ๐œ‹ (3๐‘Ÿ^2) ร— (0.02) = 4๐œ‹r2 ร— 0.02 = 4๐œ‹ (7)2 (0.02) = 3.92๐œ‹ hence, the approximate error is 3.92 ๐… m3

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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.