1. Given a cone with slant height $l$ and base radius $R$, if the maximum area of a section passing through the vertex of the cone is $\frac{l^{2}}{2}$. Then the range of $\frac{R}{l}$ is
A. $\left(0, \frac{\sqrt{2}}{2}\right)$
B. $\left(0, \frac{\sqrt{2}}{2}\right]$
C. $\left[\frac{\sqrt{2}}{2}, 1\right]$
D. $\left[\frac{\sqrt{2}}{2}, 1\right)$
1. D Since the maximum area of a section through the vertex of the circular cone is $\frac{l^{2}}{2}$, the vertex angle $\alpha$ of the axial section of the cone is in the range $\left[90^{\circ}, 180^{\circ}\right)$. Thus, $\sin \frac{\alpha}{2}=\frac{R}{l} \in\left[\frac{\sqrt{2}}{2}, 1\right)$.