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Chapter 6 Class 12 Application of Derivatives
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Ex 6.4, 6 - If radius of a sphere is measured 7 m , error 0.02 m

Ex 6.4,6 - Chapter 6 Class 12 Application of Derivatives - Part 2

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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 = βˆ†r βˆ†r = 0.02 m Volume of the sphere = V = 4/3 πœ‹π‘Ÿ^3 We need to find error in calculating the volume that is βˆ†v βˆ†V = 𝑑𝑣/π‘‘π‘Ÿ Γ— βˆ†r = 𝑑(4/3 πœ‹π‘Ÿ^3 )/π‘‘π‘Ÿ Γ— βˆ†r = 4/3 πœ‹ (𝑑(π‘Ÿ^3))/π‘‘π‘ŸΓ—βˆ†r = 4/3 πœ‹ (3π‘Ÿ^2) Γ— (0.02) = 4πœ‹r2 Γ— 0.02 = 4πœ‹ (7)2 (0.02) = 3.92πœ‹ hence, the approximate error is 3.92 𝝅 m3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.