Question 12 - Examples - Chapter 6 Class 12 Application of Derivatives

Last updated at December 16, 2024 by

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

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Question 12 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 = āˆ†r = 0.03 cm We need to find Error in calculating Volume Let Volume of sphere = V = šŸ’/šŸ‘ š…š’“^šŸ‘ āˆ“ We need to find āˆ†V Now, āˆ†V = š‘‘š‘‰/š‘‘š‘Ÿ āˆ†r = š‘‘(4/3 šœ‹š‘Ÿ^3 )/š‘‘š‘Ÿ āˆ†r = 4/3 šœ‹ (š‘‘š‘Ÿ^3)/š‘‘š‘Ÿ āˆ†r = 4/3 šœ‹ (3š‘Ÿ^2 )(0.03 ) = 4šœ‹š‘Ÿ^2(0.03) = 4šœ‹(9)2 (0.03) = 9.72š… cm3 Hence, approximate error in calculating volume is 9.72šœ‹ cm3

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