1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
  3. Approximations (using Differentiation)
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Question 6 - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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

    3. Approximations (using Differentiation)

    Finding rate of change →
Finding rate of change →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo