The outward field … has magnitude

The outward field $\mathbf{F}=\mathbf{R}/{\rho }^3$ has magnitude $|\mathbf{F}|=1/{\rho }^2$. Through an area $A$ on a sphere of radius $\rho$, the flux is ______. A spherical box has faces at ${\rho }_1$ and ${\rho }_2$ with $A={\rho }_1^2\sin \varphi d\varphi d\theta$ and $A={\rho }_2^2\sin \varphi d\varphi d\theta$. Deduce that the flux out of the box is zero, which confirms $÷\mathbf{F}=0$.

This exercise has fill-in blanks from its source book and no answer key.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.5 The Divergence Theorem, #24