3. In a regular quadrilateral pyramid $P-A B C D$, it is known that $A_{1} 、 C_{1}$ are the midpoints of $P A 、 P C$ respectively. Then
$$
\frac{V_{\text {=floor } A_{1}}-B C_{1} D}{V_{\text {regular quadrilateral pyramid } P-A B C D}}=
$$
$\qquad$
3. $\frac{1}{4}$.

Notice,
$$
\begin{array}{l}
\text { Also } V_{=B-A_{1} C_{1} P}=\frac{1}{4} V_{=} B-A C P \\
=\frac{1}{4} V_{=}-A B C=\frac{1}{8} V_{=}-A B C C .
\end{array}
$$