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

Transcript

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 3 We need to find error in calculating the volume that is v V = r = 4 3 3 r = 4 3 ( 3 ) r = 4 3 (3 2 ) (0.02) = 4 r2 0.02 = 4 (7)2 (0.02) = 3.92 hence, the approximate error is 3.92 m3