Ex 6.4, 6 - If radius of a sphere is measured 7 m , error 0.02 m - Finding approximate value- Statement questions

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Ex 6.4,6 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﷯𝜋 𝑟﷮3﷯ We need to find error in calculating the volume that is ∆v ∆V = 𝑑𝑣﷮𝑑𝑟﷯ × ∆r = 𝑑 4﷮3﷯𝜋 𝑟﷮3﷯﷯﷮𝑑𝑟﷯ × ∆r = 4﷮3﷯𝜋 𝑑( 𝑟﷮3﷯)﷮𝑑𝑟﷯×∆r = 4﷮3﷯𝜋 (3 𝑟﷮2﷯) × (0.02) = 4𝜋r2 × 0.02 = 4𝜋 (7)2 (0.02) = 3.92𝜋 hence, the approximate error is 3.92 𝝅 m3

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