Question 7 - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at December 16, 2024 by

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

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Question 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 = āˆ†š‘Ÿ āˆ†š‘Ÿ = 0.03 m Surface area of the sphere = S = 4šœ‹š‘Ÿ^2 We need to find the error in calculating the surface area āˆ† S āˆ† S = š‘‘š‘ /š‘‘š‘ŸĆ—āˆ†"r" = (š‘‘("4" šœ‹š‘Ÿ^2))/š‘‘š‘ŸĆ—āˆ†"r" = "4" šœ‹ (š‘‘(š‘Ÿ^2))/š‘‘š‘ŸĆ—āˆ†"r" = 8šœ‹r Ɨ 0.03 = 8šœ‹(9) (0.03) = 2.16šœ‹ hence the approximate error is 2.16š… m2

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