Ex 6.4,7 - Chapter 6 Class 12 Application of Derivatives

Transcript

Ex 6.4,7 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 = ∆𝑟 ∆𝑟 = 0.03 m Surface area of the sphere = S = 4𝜋 𝑟﷮2﷯ We need to find the error in calculating the surface area ∆ S ∆ S = 𝑑𝑠﷮𝑑𝑟﷯×∆r = 𝑑(4𝜋 𝑟﷮2﷯)﷮𝑑𝑟﷯×∆r = 4𝜋 𝑑( 𝑟﷮2﷯)﷮𝑑𝑟﷯×∆r = 8𝜋r × 0.03 = 8𝜋(9) (0.03) = 2.16𝜋 hence the approximate error is 2.16𝝅 m2