A cylinder A of a material of thermal conductivity `K_(1)` is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity `K_(2)`. The two ends of the combined system are maintained at two different temperature. if the effective thermal conductivity of the system is `(4K_(1) + 5K_(2))/(9)`, find the rate of outer radius of the shell to the radius of the cylinder.