Answer
$\rho\lt 1$.
Work Step by Step
The set $x^2+y^2+z^2\leq1$ is the closed sphere in $R^3$, centered at the origin. Since $$
\begin{aligned}
&x=\rho \sin \phi \cos \theta\\
&y=\rho \sin \phi \sin \theta\\
&z=\rho \cos \phi,
\end{aligned}
$$we have $$x^2+y^2+z^2=\rho^2(\sin^2\phi\cos^2\theta+\sin^2\phi\sin^2\theta+\cos^2\phi)\\ =\rho^2$$ That is, $\rho^2\leq 1$ and since $\rho$ is non negative then $\rho\lt 1$.
