\[a = 48\ см,\ \ b = \frac{5}{8}a,\]
\[\ \ h = \frac{2}{3}b,\ \ V = ?\]
\[b = 48\ :8 \cdot 5 = 5 \cdot 6 = 30\ (см).\]
\[h = 30\ :3 \cdot 2 = 2 \cdot 10 = 20\ (см).\]
\[V = a \cdot b \cdot h = 48 \cdot 30 \cdot 20 =\]
\[= 1440 \cdot 20 = 28\ 800\ \left( см^{3} \right).\]
\[Ответ:28\ 800\ см^{3}.\]