Let $\vec { F }$ Be a Smooth Vector Field $\vec { F}$

Multiple Choice

Let $\vec { F }$ be a smooth vector field.The flux of $\vec { F}$ out of a small sphere of radius r centered at the point (1, $\pi$ , 2 $\pi$ ) is 12 $\pi$ r³. Find $\operatorname { div } \vec { F }$ at (1, $\pi$ , 2 $\pi$ ) and use the result to estimate the flux of $\vec {F }$ out of the small cube of side 0.025 centered around the point (1, $\pi$ , 2 $\pi$ ) .

A) 0.000141
B) 0.005625
C) 0.000125
D) 0.00625
E) 0.25