Approximations (using Differentiation)

Chapter 6 Class 12 Application of Derivatives
Serial order wise

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### Transcript

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 = βπ βπ = 0.03 m Surface area of the sphere = S = 4ππ^2 We need to find the error in calculating the surface area β S β S = ππ /ππΓβ"r" = (π("4" ππ^2))/ππΓβ"r" = "4" π (π(π^2))/ππΓβ"r" = 8πr Γ 0.03 = 8π(9) (0.03) = 2.16π hence the approximate error is 2.16π m2

#### Davneet Singh

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.