设正方体的棱长为$1$
$1×1×6+1×1×4=10 $
$10×\frac {3}{3+4+5}=\frac {5}{2}$
$ (\frac {5}{2}−1×1×2)÷4÷1=\frac {1}{8} $
$10×\frac {4}{3+4+5}=\frac {10}{3}$
$ (\frac {10}{3}-1×1×2)÷4÷1=\frac {1}{3} $
$10×\frac {5}{3+4+5}=\frac {25}{6}$
$ (\frac {25}{6}−1×1×2)÷4÷1=\frac {13}{24}$
$ \frac {1}{8}:\frac {1}{3}:\frac {13}{24}=3:8:13 $
答$:$体积比为$3:8:13。$