14. A rectangular prism with integer edge lengths is painted red on all its surfaces, and then it is cut into small cubes with an edge length of 1. Among them, there are 40 small cubes with two red faces, and 66 small cubes with one red face. What is the volume of this rectangular prism?
【Answer】 150
【Analysis】Let the length, width, and height of this rectangular prism be $a, b, c$, respectively, then we have:
$\left\{\begin{array}{l}4[(a-2)+(b-2)+(c-2)]=40 \\ 2[(a-2)(b-2)+(a-2)(c-2)+(b-2)(c-2)]=66\end{array}\right.$, if we set $\left\{\begin{array}{l}x=a-2 \\ y=b-2 \\ z=c-2\end{array}\right.$, then $x>2, y>2, z>2$;
Rearranging, we get $\left\{\begin{array}{l}x+y+z=10 \\ x y+x z+y z=33\end{array} \Rightarrow\left\{\begin{array}{l}x=3 \\ y=3 \\ z=4\end{array} \Rightarrow\left\{\begin{array}{l}a=5 \\ b=5 \\ c=6\end{array} \Rightarrow V_{\text {rectangular prism }}=5 \times 5 \times 6=150\right.\right.\right.$.