Answer
$V\left(r_2\right)=\frac{Q}{4 \pi \varepsilon_0 r_2} $
Work Step by Step
Using the expression for $V(r)$ found in (b), we have
$
V\left(r_1\right)=\frac{\rho}{3 \varepsilon_0}\left(\frac{3 r_2^2}{2}-\frac{r_1^2}{2}-\frac{r_1^3}{r_1}\right)=\frac{\rho}{3 \varepsilon_0}\left(\frac{3 r_2^2}{2}-\frac{3 r_1^2}{2}\right)=\frac{\rho}{2 \varepsilon_0}\left(r_2^2-r_1^2\right)
$
and
$
V\left(r_2\right)=\frac{\rho}{3 \varepsilon_0}\left(\frac{3 r_2^2}{2}-\frac{r_2^2}{2}-\frac{r_1^3}{r_2}\right)=\frac{\rho}{3 \varepsilon_0}\left(r_2^2-\frac{r_1^3}{r_2}\right)=\frac{\rho}{3 \varepsilon_0 r_2}\left(r_2^3-r_1^3\right)=\frac{3 Q / 4 \pi}{3 \varepsilon_0 r_2}=\frac{Q}{4 \pi \varepsilon_0 r_2} .
$
So the solutions agree at $r=r_1$ and at $r=r_2$.
