Cho hình chóp S.ABCD, gọi M, N, P, Q lần lượt là t...

B

- Hướng dẫn giải

Ta có: \(\frac{{{V_{S.MPQ}}}}{{{V_{S.ADC}}}} = \frac{{SM}}{{SA}}.\frac{{SP}}{{SC}}.\frac{{SQ}}{{SD}} = \frac{1}{2}.\frac{1}{2}.\frac{1}{2} = \frac{1}{8}\) 

\(\frac{{{V_{S.MPN}}}}{{{V_{S.ACB}}}} = \frac{{SM}}{{SA}}.\frac{{SP}}{{SC}}.\frac{{SN}}{{SB}} = \frac{1}{2}.\frac{1}{2}.\frac{1}{2} = \frac{1}{8}\) 

Suy ra \(\frac{1}{8} = \frac{{{V_{S.MNP}}}}{{{V_{S.ADC}}}} = \frac{{{V_{S.MPN}}}}{{{V_{S.ACB}}}} = \frac{{{V_{S.MPN}} + {V_{S.MPN}}}}{{{V_{S.ADC}} + {V_{S.ACB}}}} = \frac{{{V_{S.MNPQ}}}}{{{V_{S.ABCD}}}}\) 

\( \Rightarrow {V_{S.ABCD}} = 8{V_{S.MNPQ}} = 8\)