Cho hình chóp S.ABCD

D

- Hướng dẫn giải

Chọn D.

$$\begin{gathered} V_{S.ABD}=V_{D.AOK}+V_{AOHK} \\ +V_{B.AOH}+V_{S.AHK} \\ \Rightarrow V_{AOHK}=V_{S.ABD}-(V_{AOHK} \\ +V_{B.AOH}+V_{S.AHK}) \end{gathered}$$

Ta có

$$\begin{gathered} V_{S.ABD}=\frac{1}{2}{V}_{S.ABCD}. \\ \frac{V_{S.AHK}}{V_{S.ABD}}=\frac{SH}{SB}.\frac{SK}{SD}=\frac{1}{4} \end{gathered}$$

$$\begin{gathered} \Rightarrow V_{S.AHK}=\frac{1}{4}{V}_{S.ABD} \\ =\frac{1}{8}.V_{S.ABCD} \end{gathered}$$

Tương tự

$$\begin{gathered} \Rightarrow V_{B.AOH}=\frac{1}{8}.V_{S.ABCD}, V_{D.AOK} \\ =\frac{1}{8}{V}_{S.ABCD} \end{gathered}$$

Vậy

 $$\begin{gathered} \Rightarrow V_{AOKH}=\left(\frac{1}{2}-\frac{1}{8}-\frac{1}{8}-\frac{1}{8}\right).V_{S.ABCD} \\ =\frac{1}{8}{V}_{S.ABCD} \end{gathered}$$