Câu hỏi 6

Ta có: \({V_{ABC.A'B'C'}} = {V_{M.A'B'C'}} + {V_{M.ABC}} + {V_{M.BCC'B'}}\)

\(\begin{array}{l} \Leftrightarrow {V_{ABC.A'B'C'}} = 2{V_{MABC}} + V = 2.\dfrac{1}{3}d\left( {M;\,\,\left( {ABC} \right)} \right).{S_{ABC}} + V\\ \Leftrightarrow {V_{ABC.A'B'C'}} = 2.\dfrac{1}{3}.\dfrac{1}{2}d\left( {A';\,\,\left( {ABC} \right)} \right).{S_{ABC}} + V\\ \Leftrightarrow {V_{ABC.A'B'C'}} = \dfrac{1}{3}{V_{ABC.A'B'C'}} + V\\ \Rightarrow \dfrac{2}{3}{V_{ABC.A'B'C'}} = V\\ \Leftrightarrow {V_{ABC.A'B'C'}} = \dfrac{3}{2}V.\end{array}\)

Chọn C.