Aloha :)
$$\Delta R=\sqrt{\left(\frac{\partial R}{\partial L}\,\Delta L\right)^2+\left(\frac{\partial R}{\partial D}\,\Delta D\right)^2}=\sqrt{\left(\frac{\rho}{\pi\cdot D}\,\Delta L\right)^2+\left(-\frac{\rho\cdot L}{\pi\cdot D^2}\,\Delta D\right)^2}$$$$\phantom{\Delta R}=\sqrt{\left(R\,\frac{\Delta L}{L}\right)^2+\left(-R\,\frac{\Delta D}{D}\right)^2}=R\,\sqrt{\left(\frac{\Delta L}{L}\right)^2+\left(\frac{\Delta D}{D}\right)^2}$$