Cho hình chóp S.ABCD. Gọi...

C

- Hướng dẫn giải

Đáp án C

Ta có: $\frac{V_{S.A\text{'}B\text{'}C\text{'}}}{V_{S.ABC}}=\frac{SA\text{'}}{SA}.\frac{SB\text{'}}{SB}.\frac{SC\text{'}}{SC}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}=\frac{1}{8}$

$\Rightarrow V_{S.A\text{'}B\text{'}C\text{'}}=\frac{1}{8}{V}_{S.ABC}\left(1\right)$

$\frac{V_{S.A\text{'}D\text{'}C\text{'}}}{V_{S.ADC}}=\frac{SA\text{'}}{SA}.\frac{SD\text{'}}{SD}.\frac{SC\text{'}}{SC}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}=\frac{1}{8}$

$\Rightarrow V_{S.A\text{'}D\text{'}C\text{'}}=\frac{1}{8}{V}_{S.ADC}\left(2\right)$

Từ (1) và (2) $\Rightarrow V_{S.A\text{'}B\text{'}C\text{'}D\text{'}}=V_{S.A\text{'}B\text{'}C\text{'}}+V_{S.A\text{'}D\text{'}C\text{'}}=\frac{1}{8}\left(V_{S.ABC}+V_{S.ADC}\right)$

$=\frac{1}{8}{V}_{S.ABCD}\Rightarrow \frac{V_{S.A\text{'}B\text{'}C\text{'}D\text{'}}}{V_{S.ABCD}}=\frac{1}{8}$