Question 6 - Finding approximate value- Statement questions - Chapter 6 Class 12 Application of Derivatives

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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 = ∆r ∆r = 0.02 m Volume of the sphere = V = 4/3 𝜋𝑟^3 We need to find error in calculating the volume that is ∆v ∆V = 𝑑𝑣/𝑑𝑟 × ∆r = 𝑑(4/3 𝜋𝑟^3 )/𝑑𝑟 × ∆r = 4/3 𝜋 (𝑑(𝑟^3))/𝑑𝑟×∆r = 4/3 𝜋 (3𝑟^2) × (0.02) = 4𝜋r2 × 0.02 = 4𝜋 (7)2 (0.02) = 3.92𝜋 hence, the approximate error is 3.92 𝝅 m3