Let $r = (x, y, z)$, $r = |r|$, and $\hat{r} = \frac{r}{r}$. We have shown that $\vec{F} = \frac{1}{(x^2 + y^2 + z^2)^{3/2}}(x, y, z)$ satisfies $\nabla \cdot \vec{F} = 0$ on its domain.
On which solids below is it appropriate to apply Gauss' Theorem to conclude that the outward flux of $\vec{F} = \frac{1}{(x^2 + y^2 + z^2)^{3/2}}(x, y, z)$ through the boundary of the solid is 0? Select all that apply.
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | x^2 + y^2 - 1 \le z \le 3\}$
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | x^2 + y^2 + (z - 2)^2 \le 1\}$
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | x^2 + y^2 + (z - 1)^2 \le 4\}$
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | 1 + x^2 + y^2 \le z \le 5\}$
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | \sqrt{x^2 + y^2} - 1 \le z \le 1\}$
$\square$ $\{(x, y, z) \in \mathbb{R}^3 | x^2 + y^2 + z^2 \le 1\}$
