Answer
$\frac{8}{9}\ m-tons$.
Work Step by Step
Step 1. Assume $L\ (m-tons)$ is the maximum load a cylindrical column of circular cross section.
Step 2. Assume $d\ (m)$ is the diameter and $h\ (m)$ is the height.
Step 3. From the given conditions, we have $L=kd^4/h^2$ and $8=k(1)^4/(9)^2$, thus $k=648$
Step 4. For $d=\frac{2}{3}\ (m)$ and $h=12\ (m)$, we have $L=(648)(\frac{2}{3})^4/(12)^2=\frac{8}{9}\ m-tons$.
