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If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area
Concept:Let the radius of a sphere is r meters,The surface area of Sphere(A) = 4?r2Calculation:Given: Radius of a sphere = 6 m and ?r = 0.02mNow, the volume of the sphere is given by,A = 4?r2Differentiating with respect to r, we get\(\rm = \frac{{{\rm{dS}}}}{{{\rm{dr}}}} = 8? r\)= dS = 8?r?dr= dS = 8??6?(0.02)= dS = 0.96 square meters
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