Solution
= Solution
Take the <sphere>'s outward normal. Since $F=k(x,y,z)$ with constant $k$, its <divergence> is $3k$. The <divergence theorem> gives
$$
\boxed{\int_SF\cdot dS=3k\,\frac{4\pi r^3}{3}=4\pi kr^3.}
$$
The translated <centre> does not enter the answer, because the <divergence> is constant. Equivalently the constant field produced by translating coordinates has zero net <flux> through a closed <sphere>. The inward orientation would negate the result.