A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted by $1$ and the inner surface of the cube is denoted by $2$. The view factor $F_{22}$ for radiation heat transfer is ______ ($\textit{rounded off to two decimal places}$).