Cho hình chóp tứ giác S.ABCD . Gọi V là thể tích khối chóp S.ABCD.

* Hướng dẫn giải

\(\begin{array}{l}
\frac{{{V_{S.A'B'C'}}}}{{{V_{S.ABC}}}} = \frac{{SA'}}{{SA}}.\frac{{SB'}}{{SB}}.\frac{{SC'}}{{SC}} = \frac{1}{{64}}\\
\frac{{{V_{S.A'D'C'}}}}{{{V_{S.ADC}}}} = \frac{{SA'}}{{SA}}.\frac{{SD'}}{{SD}}.\frac{{SC'}}{{SC}} = \frac{1}{{64}}
\end{array}\)

Suy ra \(\begin{array}{l}
\frac{{{V_{S.A'B'C'}}}}{{{V_{S.ABC}}}} = \frac{{SA'}}{{SA}}.\frac{{SB'}}{{SB}}.\frac{{SC'}}{{SC}} = \frac{1}{{64}}\\
\frac{{{V_{S.A'D'C'}}}}{{{V_{S.ADC}}}} = \frac{{SA'}}{{SA}}.\frac{{SD'}}{{SD}}.\frac{{SC'}}{{SC}} = \frac{1}{{64}}
\end{array}\)

hay \({V_{S.A'B'C'D'}} = \frac{1}{{64}}{V_{S.ABCD}} = \frac{V}{{64}}\)