Cho lăng trụ \(ABC.

* Hướng dẫn giải

Ta có: \(C{C_1}//{\rm{A}}{{\rm{A}}_1} \Rightarrow C{C_1}//\left( {AB{B_1}{A_1}} \right) \Rightarrow d\left( {C{C_1};\left( {AB{B_1}{A_1}} \right)} \right) = d\left( {{C_1};\left( {AB{B_1}{A_1}} \right)} \right)\) 

\( \Rightarrow {V_{{C_1}.AB{B_1}{A_1}}} = \frac{1}{3}d\left( {{C_1};AB{B_1}{A_1}} \right).{S_{AB{B_1}{A_1}}} = \frac{1}{3}.6.4 = 8\)

Ta có: \({V_{{C_1}.ABC}} = \frac{1}{3}{V_{ABC.{A_1}{B_1}{C_1}}} \Rightarrow {V_{{C_1}.AB{B_1}{A_1}}} = \frac{2}{3}{V_{ABC.{A_1}{B_1}{C_1}}}\)

\( \Rightarrow {V_{ABC.{A_1}{B_1}{C_1}}} = \frac{3}{2}{V_{{C_1}.AB{B_1}{A_1}}} = \frac{3}{2}.8 = 12\)