Answer
(a) $V = 65.6 \,\text{V}$
(b) $V = 131 \,\text{V}$
(c) $V = 131 \,\text{V}$
Work Step by Step
(a) The radius of the sphere is $R$ = 24 cm. So, at $r$ = 48 cm the potential outside the sphere is given by
\begin{align*}
V &= \dfrac{1}{4 \pi \epsilon_{\circ}} \dfrac{q}{r}\\
&= (9.0 \times 10^{9} \mathrm{~N\cdot m^{2}/C^{2}}) \dfrac{(3.50 \times 10^{-9} \,\text{C})}{0.48 \,\text{m}}\\
&= \boxed{65.6 \,\text{V}}
\end{align*}
(b) when $r = R $ = 24 cm the potential inside the sphere is given by
\begin{align*}
V &= \dfrac{1}{4 \pi \epsilon_{\circ}} \dfrac{q}{R}\\
&= (9.0 \times 10^{9} \mathrm{~N\cdot m^{2}/C^{2}}) \dfrac{(3.50 \times 10^{-9} \,\text{C})}{0.24 \,\text{m}}\\
&= \boxed{131 \,\text{V}}
\end{align*}
(c) When $r$ = 12 cm the potential is the same everywhere, so at $r$ = 12 cm also, the potential is the same for $r$ = 24 cm
$$\boxed{V = 131 \,\text{V}}$$
