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

A

- 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 ${V_{S.A'B'C'D'}} = \frac{1}{{64}}{V_{S.ABCD}} = \frac{V}{{64}}$