4. Given that the tetrahedron $A B C D$ is inscribed in sphere $O$, and $A D$ is the diameter of sphere $O$. If $\triangle A B C$ and $\triangle B C D$ are both equilateral triangles with side length 1, then the volume of the tetrahedron $A B C D$ is ( )
A: $\frac{\sqrt{2}}{6}$
B: $\frac{\sqrt{2}}{12}$
C: $\frac{\sqrt{3}}{6}$
D: $\frac{\sqrt{3}}{12}$
荅暴 B.
解析 Four-sided pyramid with an isosceles right $\triangle A B D$ as the base, and height $\frac{\sqrt{2}}{2}$, so the volume is $\frac{1}{3} \times \frac{\sqrt{2}}{2} \times \frac{1}{2}=\frac{\sqrt{2}}{12}$.