11.016. The base of a quadrilateral pyramid is a rectangle with a diagonal equal to $b$, and the angle between the diagonals is $60^{\circ}$. Each of the lateral edges forms an angle of $45^{\circ}$ with the base plane. Find the volume of the pyramid.
## Solution.

Given $B D=b, \angle A O B=60^{\circ}$ (Fig. 11.14); hence $A B=\frac{b}{2}$, $A D=\frac{b \sqrt{3}}{2}$. Therefore, $S_{\text {base }}=A B \cdot A D=\frac{b^{2} \sqrt{3}}{4}$. Since $\angle S A O=\angle S B O=\angle S C O=\angle S D O=45^{\circ}$, $S O$ is the height of the pyramid and $S O=\frac{b}{2}$. Thus, $V=\frac{1}{3} S_{\text {base }} \cdot S O=\frac{b^{3} \sqrt{3}}{24}$.

Answer: $\frac{b^{3} \sqrt{3}}{24}$.