Example 25 - If radius of a sphere is 9 cm with error 0.03 cm

Example 25 - Chapter 6 Class 12 Application of Derivatives - Part 2

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

Transcript

Example 25 If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.Given Radius of sphere = r = 9 cm Error in radius = โˆ†r = 0.03 cm We need to find Error in calculating Volume Let Volume of sphere = V = ๐Ÿ’/๐Ÿ‘ ๐…๐’“^๐Ÿ‘ โˆด We need to find โˆ†V Now, โˆ†V = ๐‘‘๐‘‰/๐‘‘๐‘Ÿ โˆ†r = ๐‘‘(4/3 ๐œ‹๐‘Ÿ^3 )/๐‘‘๐‘Ÿ โˆ†r = 4/3 ๐œ‹ (๐‘‘๐‘Ÿ^3)/๐‘‘๐‘Ÿ โˆ†r = 4/3 ๐œ‹ (3๐‘Ÿ^2 )(0.03 ) = 4๐œ‹๐‘Ÿ^2(0.03) = 4๐œ‹(9)2 (0.03) = 9.72๐… cm3 Hence, approximate error in calculating volume is 9.72๐œ‹ cm3

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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.