Đáp án:
\({V_{S.MNC}} = 3{a^3}.\)
Giải thích các bước giải:
\(\begin{array}{l}
2SM = 3AM \Rightarrow \frac{{SM}}{{AM}} = \frac{3}{2} \Leftrightarrow \frac{{SM}}{{SM + AM}} = \frac{3}{{3 + 2}} \Leftrightarrow \frac{{SM}}{{SA}} = \frac{3}{5}\\
\overrightarrow {BN} = - 2\overrightarrow {SN} \Rightarrow \frac{{SN}}{{SB}} = \frac{1}{3}\\
\Rightarrow \frac{{{V_{S.MNC}}}}{{{V_{S.ABC}}}} = \frac{{SM}}{{SA}}.\frac{{SN}}{{SB}} = \frac{3}{5}.\frac{1}{3} = \frac{1}{5}\\
\Rightarrow {V_{S.MNC}} = \frac{1}{5}{V_{S.ABC}} = \frac{1}{5}.15{a^3} = 3{a^3}.
\end{array}\)
