Question Bank - Mathematics

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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

A.
0.48 square meters
B.
0.96 square meters
C.
1.20 square meters
D.
0.72 square meters

Solution:

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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