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Approximations (using Differentiation)

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

Last updated at May 29, 2023 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 = βˆ†π‘Ÿ βˆ†π‘Ÿ = 0.03 m Surface area of the sphere = S = 4πœ‹π‘Ÿ^2 We need to find the error in calculating the surface area βˆ† S βˆ† S = 𝑑𝑠/π‘‘π‘ŸΓ—βˆ†"r" = (𝑑("4" πœ‹π‘Ÿ^2))/π‘‘π‘ŸΓ—βˆ†"r" = "4" πœ‹ (𝑑(π‘Ÿ^2))/π‘‘π‘ŸΓ—βˆ†"r" = 8πœ‹r Γ— 0.03 = 8πœ‹(9) (0.03) = 2.16πœ‹ hence the approximate error is 2.16𝝅 m2

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