B. \(\frac{{{a^3}\sqrt 3 }}{9}\).
C. \(\frac{{{a^3}\sqrt 2 }}{2}\).
D. \(\frac{{{a^3}\sqrt 2 }}{3}\).
Lời giải
Ta có \(\left\{ \begin{array}{l}BC \bot AB\\BC \bot SA\end{array} \right. \Rightarrow BC \bot (SAB)\)
\( \Rightarrow \left\{ \begin{array}{l}BC \bot SB\\BC \bot AB\end{array} \right. \Rightarrow \widehat {((SBC),(ABCD))} = \widehat {SBA} = {30^^\circ }\)
\(\tan {30^^\circ } = \frac{{SA}}{{AB}} \Rightarrow SA = AB \cdot \tan {30^^\circ } = \frac{a}{{\sqrt 3 }}\)
\({V_{S.ABCD}} = \frac{1}{3}SA \cdot {S_{ABCD}} = \frac{1}{3}\frac{a}{{\sqrt 3 }} \cdot {a^2} = \frac{{{a^3}\sqrt 3 }}{9}\).
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