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Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral  of a vector field  over the entire surface A of the cube is ______.
  • a)
    14
  • b)
    27
  • c)
    28
  • d)
    31
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider a cube of unit edge length and sides parallel to co-ordinate ...
Given : Vector field, 
Surface integral, 
where, A is entire surface A of the cube.
By divergence theorem,

By equation (i),

Volume of cube, V =a3 (with a = 1 unit edge length)
I = 14 x a3
I = 14 x 1
I = 14
Hence, the correct option is (A).
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