Suppose $\bf{F}$ is a radial force field, $S_{1}$ is a sphere of radius $3$ centered at the origin, and the flux integral $\displaystyle \int\!\!\int_{S_{1}} \mathbf{F} \cdot d\mathbf{S} = 6$.
Let $S_{2}$ be a sphere of radius $9$ centered at the origin, and consider the flux integral $\displaystyle \int\!\!\int_{S_{2}} \mathbf{F} \cdot d\mathbf{S}$.

(A) If the magnitude of $\mathbf{F}$ is inversely proportional to the square of the distance from the origin,what is the value of $\displaystyle \int\!\!\int_{S_{2}} \mathbf{F} \cdot d\mathbf{S}$?

(B) If the magnitude of $\bf{F}$ is inversely proportional to the cube of the distance from the origin, what is the value of $\displaystyle \int\!\!\int_{S_{2}} \mathbf{F} \cdot d\mathbf{S}$?