$\begin{aligned} & Q=\int_0^R 4 \pi r^2 \cdot \frac{A}{r^2} e^{2 r / a} d r \\ & =\left.\frac{4 \pi A a}{-2} e^{2 r / a}\right|_0 ^R=2 \pi a A\left[1-e^{\frac{-2 R}{a}}\right] \\ & =e^{-2 R / a}=1-\frac{Q}{2 \pi a A} \\ & \Rightarrow e^{\frac{2 R}{a}}=\frac{1}{\left(1-\frac{Q}{2 \pi a A}\right)} \\ & \Rightarrow R=\frac{a}{2} \ln =\frac{1}{\left(1-\frac{Q}{2 \pi a A}\right)} \\ & \Rightarrow\end{aligned}$