Cho hình chóp $S.ABC\text{D}$ có đáy $ABC\text{D}$ là hình vuông...

Ta có\left\{ \begin{aligned}
& \left( SAB \right)\bot \left( ABC\text{D} \right) \\
& \left( SAB \right)\cap \left( ABC\text{D} \right)=AB \\
& BC\bot AB \\
\end{aligned} \right. \Rightarrow BC\bot \left( SAB \right)\Rightarrow BC\bot SA \left( 1 \right)SABS\Rightarrow SB\bot SA\left( 2 \right)\left( 1 \right);\left( 2 \right)\Rightarrow SA\bot \left( SBC \right)\Rightarrow SA\bot SCOABC\text{D}OA=OB=OC=OS=\dfrac{a\sqrt{2}}{2}OS.ABC\text{D}S.ABC\text{D}V=\dfrac{4}{3}\pi {{\left( \dfrac{a\sqrt{2}}{2} \right)}^{3}}=\dfrac{\pi {{a}^{3}}\sqrt{2}}{3}$.